4.7-74x*43h= resolution
mustang 74x
you need to find the value of X first before you can solve this equation
8x - 4x + 7 = 94x + 7 = 94x = 9-74x = 2x = 4/2x = 1/2x = 0.5
If that's 3x2 + 7x + 2, the answer is (x + 2)(3x + 1)
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Let x = first integer2nd integer = x + 13rd integer = x + 2x + (x +1) + (x + 2) = x - 713x + 3 = x - 713x = x - 742x = -74x = -371st Integer = -372nd Integer = -363rd Integer = -35(-37) + (-36) + (-35) = -108-108 + 71 = -37
3/5 + 5x/2 = 8Multiply each term by 53 + 25x/2 = 40Multiply each term by 26 + 25x = 8025x = 80 - 625x = 74x = 74 / 25OR3/5 + 5x/2 = 85x/2 = 8 - 3/55x/2 = 40/5 - 3/55x/2 = 37/55x = 37/5 * 25x = 74/5x = 74/5 * 1/5x = 74/25
Let's represent the two consecutive numbers as x and x+1. The sum of these two numbers is x + (x+1) = 2x + 1. Given that the sum is 75, we have the equation 2x + 1 = 75. Solving for x, we find x = 37. Therefore, the two consecutive numbers are 37 and 38, and their sum is indeed 75.
-x + y = 24x - 3y = -7-x + y = 2 (add x to both sides)y = x + 2 (substitute x + 2 for y into the second equation of the system)4x - 3y = -74x - 3(x + 2) = -7 (solve for x)4x - 3x - 6 = -7x - 6 = -7 (add 6 to both sides)x = -1y = x + 2 (substitute -1 for x)y = -1 + 2y = 1Thus (-1, 1) is the solution of the given system of the equations.
Let the first odd integer be x, so the other consecutive odd integer is x + 2. So we have:x^2 + (x + 2)^2 = 74x^2 + x^2 + 4x + 4 = 742x^2 + 4x + 4 - 74 = 74 - 742x^2 + 4x - 70 = 0 divide by 2 to both sidesx^2 + 2x - 35 = 0(x + 7)(x - 5) = 0x + 7 = 0 or x - 5 = 0x + 7 - 7 = 0 -7 or x - 5 + 5 = 0 + 5x = -7 or x = 5Thus, the first odd integer would be -7 or 5, and the second consecutive odd integer would be -5 (-7 + 2) or 7 (5 + 2).Check:
In the special case when a =1, the factoring method results in finding 2 NUMBERS knowing their sum and their product. The process is simple. However, when the constants a, b, c are large numbers, and contain themselves many factors, then the factoring method becomes complicated and takes long time in the process. For examples, solving these equations by the factoring method will take lot of time because of the high number of permutations: (6x^2 - 11x - 35 = 0) ; (45x^2 + 74x - 55 = 0) ; (45x^2 - 152x - 36 = 0); (12x^2 + 5x - 72 = 0) There is a new method, called Diagonal Sum Method, that can quickly and directly give the 2 roots, WITHOUT HAVING TO FACTOR THE EQUATION. The innovative concept of the new method is finding 2 FRACTIONS knowing their sum (-b/a) and their product (c/a). It is faster, more convenient than the factoring method since it requires fewer permutations by using the rule of signs for real roots. It is applicable whenever the equation can be factored. So, I advise you to proceed solving any quadratic equation in 2 steps. First step, use the Diagonal Sum method to solve it. It usually takes fewer than 3 trials. If it fails, then the quadratic formula must be used in second step. See book title:" New method for solving quadratic equations and inequalities" (Trafford Publishing 2009)