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Simplifying (2x + -13)(2x + -7) = (2x + -7) Reorder the terms: (-13 + 2x)(2x + -7) = (2x + -7) Reorder the terms: (-13 + 2x)(-7 + 2x) = (2x + -7) Multiply (-13 + 2x) * (-7 + 2x) (-13(-7 + 2x) + 2x * (-7 + 2x)) = (2x + -7) ((-7 * -13 + 2x * -13) + 2x * (-7 + 2x)) = (2x + -7) ((91 + -26x) + 2x * (-7 + 2x)) = (2x + -7) (91 + -26x + (-7 * 2x + 2x * 2x)) = (2x + -7) (91 + -26x + (-14x + 4x2)) = (2x + -7) Combine like terms: -26x + -14x = -40x (91 + -40x + 4x2) = (2x + -7) Reorder the terms: 91 + -40x + 4x2 = (-7 + 2x) Remove parenthesis around (-7 + 2x) 91 + -40x + 4x2 = -7 + 2x Solving 91 + -40x + 4x2 = -7 + 2x Solving for variable 'x'. Reorder the terms: 91 + 7 + -40x + -2x + 4x2 = -7 + 2x + 7 + -2x Combine like terms: 91 + 7 = 98 98 + -40x + -2x + 4x2 = -7 + 2x + 7 + -2x Combine like terms: -40x + -2x = -42x 98 + -42x + 4x2 = -7 + 2x + 7 + -2x Reorder the terms: 98 + -42x + 4x2 = -7 + 7 + 2x + -2x Combine like terms: -7 + 7 = 0 98 + -42x + 4x2 = 0 + 2x + -2x 98 + -42x + 4x2 = 2x + -2x Combine like terms: 2x + -2x = 0 98 + -42x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(49 + -21x + 2x2) = 0 Factor a trinomial. 2((7 + -2x)(7 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -2x)' equal to zero and attempt to solve: Simplifying 7 + -2x = 0 Solving 7 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2x = 0 + -7 -2x = 0 + -7 Combine like terms: 0 + -7 = -7 -2x = -7 Divide each side by '-2'. x = 3.5 Simplifying x = 3.5Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {3.5, 7}
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