x2 + 6x = 16=> x2 + 6x - 16 = 0=> x2 + 8x -2x - 16 = 0=> (x+8)(x-2) = 0=> x = -8 or x = 2So, the solutions of the quadratic equation x2 + 6x = 16 are -8 and 2.
your equation is this... 2x3 + 11x = 6x 2x3 + 5x = 0 x(2x2 + 5) = 0 x = 0 and (5/2)i and -(5/2)i
x2 + 6x = 16x2 + 6x - 16 = 0(x + 8)(x - 2) = 0x + 8 = 0 or x - 2 = 0x = -8 or x = 2Since it is given that x > 0, then x = -8 is not a solution of the equation. Thus, the only solution is x = 2.
Once you find the y-intercept(s) you'll be steps away from finding the x-intercept(s). The original equation is 6x - 3y = 18.Step 1 is to solve for y by isolating y on one side of the equation.6x - 3y = 18-3y = 18 - 6x-3y = -6x + 18The reason I reorganized the terms, is so that the equation is in the Slope-Intercept form.y = (-6x/-3) + (18/-3)y = 2x + (-6)y = 2x - 6This equation is in the Slope-Intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. So the y-intercept is -6. Now onto the x-intercept. To get x-intercept(s), keep the equation in the Slope-Intercept form and set y equal to zero.y = 2x - 60 = 2x - 60 + 6 = 2x6 = 2x6/2 = x3 = xSo the x-intercept is 3. Now what does these two intercepts tell you? On a graph with a y- and x-axis, when x = 0 then y = -6, which means one of the points on your line is at (0 , -6). The same thing is true for the x-intercept. When y = 0 then x = 3, and that is where your second point is, at (3 , 0). Connect those two points and you'll have your line.
2x -3 - 6x = 0 -3 = 6x - 2x -3 = 4x x = -3/4
From what i understand the equation is like this; (3 * 2 ) + 6x + 24 = 0 6 + 6x +24 = 0 6x = - 24 - 6 6x = - 30 x = - 5
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Lets say that your equation is 2(3x + 1) To make a flow chart you need to make circles ( depending on how long the equation is) and arrows ex. 0->0->0-> etc. first on the first circle put the number 2. then on the arrow the number and the operation need to ex. multiply by 2 ( in this case x 3 times multiply) then on the next circle you should have 6x ( 2 multiplied by 3x=6x). Then do the remaining ( add 1 for this equation) 6x+1= 6x=1 so this is how you simplify the equation from 2(3x + 1)+ 6x+1
The 'answer' is the number that 'x' must be in order to make the equation true.(x + 3) (x + 3) = 36Expand the left side:x2 + 6x + 9 = 36Subtract 36 from each side:x2 + 6x - 27 = 0Factor the left side:(x + 9) (x - 3) = 0This equation is true if either factor = 0:x + 9 = 0 ===> x = -9x - 3 = 0 ===> x = 3Both values for 'x' are "answers" to the original equation.
We call a solution any value of the variable which satisfies the given equation. If the number of values you get (which always satisfy the equation) is a finite number, then the equation is sometimes true (meaning it is true only for those values you got). ex. x + 3 = 5 is true only when x is 2. x2 - 5 = 4 is true only when x is -3 or 3. √x = 7 is true only when x is 49. (check:) 2(3x - 1) = 6x - 2 is always true, meaning for any value that x can take on, both sides becomes equal when x is replaced by it. 2(3x - 1) = 6x - 26x - 2 = 6x - 2 (both sides seems to be equal) , or subtract 6x and add 2 to both sides 0 = 0 a true statement. Since 0 = 0 is an equivalent statement to the original equation and it is a true one, then the original equation must be also a true statement. Thus, there are infinitely many solutions for the given equation. Therefore, the given equation is always true. Sometimes, before you start to solve an equation, you need to exclude some value(s) for the variable of being a solution, because they can make the equation undefined. For example, if the variable happens to be in the denominator, you have to exclude all the values of the variable that make the denominator equal to zero.
6x + 5 = 0 (I'm assuming) 6x = -5x = -5/6
9x2+6x-7 = 0 Using the quadratic equation formula:- x = 0.6094757082 or x = -1.276142375
x2 + 6x = 16=> x2 + 6x - 16 = 0=> x2 + 8x -2x - 16 = 0=> (x+8)(x-2) = 0=> x = -8 or x = 2So, the solutions of the quadratic equation x2 + 6x = 16 are -8 and 2.
Given, that 4x + 6 = 6x - 12; then, (6x - 12) - (4x + 6) = 0, 2x - 18 = 0, and 2x = 18. Thus, x = 9. Checking, we substitute 9 for x in the equation: 4(9) + 6= 6(9) - 12; whence, 36 + 6 = 54 - 12, and 42 = 42, which is patently true. What this means is that the original equation is true exactly when x = 9; otherwise, it is false. We call 'x = 9' the solution to the given equation.
sqrt(6x + 1) = (x - 1)Square each side of the equation:6x + 1 = (x - 1)26x + 1 = x2 - 2x + 1Subtract 6x from each side:1 = x2 - 8x + 1Subtract 1 from each side:x2 - 8x = 0Factor the left side:x (x - 8) = 0This equation is true if [ x = 0 ] and also if [ x = 8 ]. We'll have to checkboth of them and see if they solve the original equation.Check (x = 0) :sqrt(6x + 1) = sqrt(1) = +1 or -1(x - 1) = (0 - 1) = -1 yay!Check (x = 8) :sqrt(6x + 1) = sqrt(48 + 1) = sqrt(49) = +7 or -7(x - 1) = (8 - 1) = 7 yay!Both (x = 0) and (x = 8) make the original equation a true statement,so those are your solutions.
Assume the question refers to solving the quadratic equation 6x2 +21x - 45 = 0, then :-This equation can be factored 6x2 + 21x - 45 = (6x - 9)(x + 5) = 0This holds true when either 6x - 9 or x + 5 = 0When 6x - 9 = 0 then x = 9/6 = 1.5 : When x + 5 = 0 then x = -5
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