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Simplifying x2 + (x + -2)(x + -2) = 74 Reorder the terms: x2 + (-2 + x)(x + -2) = 74 Reorder the terms: x2 + (-2 + x)(-2 + x) = 74 Multiply (-2 + x) * (-2 + x) x2 + (-2(-2 + x) + x(-2 + x)) = 74 x2 + ((-2 * -2 + x * -2) + x(-2 + x)) = 74 x2 + ((4 + -2x) + x(-2 + x)) = 74 x2 + (4 + -2x + (-2 * x + x * x)) = 74 x2 + (4 + -2x + (-2x + x2)) = 74 Combine like terms: -2x + -2x = -4x x2 + (4 + -4x + x2) = 74 Reorder the terms: 4 + -4x + x2 + x2 = 74 Combine like terms: x2 + x2 = 2x2 4 + -4x + 2x2 = 74 Solving 4 + -4x + 2x2 = 74 Solving for variable 'x'. Reorder the terms: 4 + -74 + -4x + 2x2 = 74 + -74 Combine like terms: 4 + -74 = -70 -70 + -4x + 2x2 = 74 + -74 Combine like terms: 74 + -74 = 0 -70 + -4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-35 + -2x + x2) = 0 Factor a trinomial. 2((-5 + -1x)(7 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -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 = {-5, 7}
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