x2 - 18x + 72 = 0
(x - 6)(x - 12) = 0
x ∈ {6, 12}
x2 - 21x = 72x2 - 21x - 72 = 0(x - 24) (x + 3) = 0x = 24x = -3
As an equation if: 6x = 72 then x = 12
2x2 + 6x - 8 = 72 ∴ 2x2 + 6x + 64 =0 ∴ x2 + 3x + 32 = 0 This can not be factored, as x is not equal to any integer. Using the quadratic equation, we find that: x = -3/2 ± √119 / 2i
I assume you mean; X^2 - 72X - 735 = 0 The only way I would do this is by the quadratic formula discriminant (-72)^2 - 4(1)(-735) = 8124 and means two real roots X = - b (+/-) sqrt(b^2-4ac)/2a a = 1 b = - 72 c = - 735 X = - (-72) (+/-) sqrt[(-72)^2 - 4(1)(-735)]/2(1) X = 72 (+/-) sqrt(8124)/2 X = [72 (+/-) 2sqrt(2031)]/2 Ugly, but true.
Solving quadratic equations by the new Transforming Method. It proceeds through 3 Steps. STEP 1. Transform the equation type ax^2 + bx + c = 0 (1) into the simplified type x^2 + bx + a*c = 0 (2), with a = 1, and with C = a*c. STEP 2. Solve the transformed equation (2) by the Diagonal Sum Method that immediately obtains the 2 real roots y1, and y2. STEP 3. Divide both y1, and y2 by the coefficient a to get the 2 real roots of the original equation (1): x1 = y1 /a, and x2 = y2/a. Example 1. Solve: 12x^2 + 5x - 72 = 0 (1). Solve the transformed equation: x^2 + 5x - 864 = 0. Roots have different signs (Rule of Signs). Compose factor pairs of a*c = -864 with all first numbers being negative. Start composing from the middle of the factor chain to save time. Proceeding:.....(-18, 48)(-24, 36)(-32, 27). This last sum is -32 + 27 = -5 = -b. Then, the 2 real roots of (2) are: y1 = -32, and y2 = 27. Back to the original equation (1), the 2 real roots are: x1 = y1/a = -32/12 = -8/3, and x2 = y2/a = 27/12 = 9/4. Example 2. Solve 24x^2 + 59x + 36 = 0 (1). Solve the transformed equation x^2 + 59x + 864 = 0 (2). Both roots are negative. Compose factor pairs of a*c = 864 with all negative numbers. To save time, start composing from the middle of the factor chain. Proceeding:....(-18, -48)(-24, -36)(-32, -27). This last sum is -59 = -b. Then 2 real roots of equation (2) are: y1 = -32 and y2 = -27. Back to the original equation (1), the 2 real roots are: x1 = y1/24 = -32/24 = -4/3, and x2 = y2/24 = -27/24 = -9/8. To know how does this new method work, please read the article titled: "Solving quadratic equations by the new Transforming Method" in related links.
18x + 12y = 72 to get x-int. put y=0 18x + (12)(0) = 72 18x = 72 x = 4 your x-intercept is 4. this is the place where the line goes through the x-axis.
let 2 consecutive numbers be x and x+1, so product will be x^2+x = 72 i.e x^2 + x - 72 = 0 finding roots of quadratic equation x= -9 or x = 8 x = 8 satisfies given condition so is the answer.
Using the quadratic equation formula the value of x is -8 or 5
The expression "5n^2 + 31n - 72" is a quadratic polynomial in terms of the variable ( n ). It can be analyzed using methods such as factoring, completing the square, or applying the quadratic formula to find its roots. If you need specific information about its properties or solutions, please clarify!
x2 - 21x = 72x2 - 21x - 72 = 0(x - 24) (x + 3) = 0x = 24x = -3
(x+9)^2 =x^2 + 9 X^2 + 18x + 81 = X^2 +9 18X + 72 = 0 18X = -72 X =- 4
(-1.2,0),(1.2,0)v(0, -72)50x^2-72=0 factor out 22(25x^2-36)=02(5x+6)(5x-6)=0x=-6/5 and x=6/5The average of these two is zero, substitute that into the equation and you get -72.
(1/2, 71 and 3/4)or(0.5, 71.75)
I gotchu homie: It's The equation has x = 4 and x = -4 as its only solutions.
The numbers are: 3.51041215 and -20.51041215 A more accurate answer can be found by using the quadratic equation formula
As an equation if: 6x = 72 then x = 12
72-4*4*4 = -15 The discriminant is less than zero so there's no solutions to the quadratic equation.