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Simplifying x2 + (x + 7)(x + 7) = 25 Reorder the terms: x2 + (7 + x)(x + 7) = 25 Reorder the terms: x2 + (7 + x)(7 + x) = 25 Multiply (7 + x) * (7 + x) x2 + (7(7 + x) + x(7 + x)) = 25 x2 + ((7 * 7 + x * 7) + x(7 + x)) = 25 x2 + ((49 + 7x) + x(7 + x)) = 25 x2 + (49 + 7x + (7 * x + x * x)) = 25 x2 + (49 + 7x + (7x + x2)) = 25 Combine like terms: 7x + 7x = 14x x2 + (49 + 14x + x2) = 25 Reorder the terms: 49 + 14x + x2 + x2 = 25 Combine like terms: x2 + x2 = 2x2 49 + 14x + 2x2 = 25 Solving 49 + 14x + 2x2 = 25 Solving for variable 'x'. Reorder the terms: 49 + -25 + 14x + 2x2 = 25 + -25 Combine like terms: 49 + -25 = 24 24 + 14x + 2x2 = 25 + -25 Combine like terms: 25 + -25 = 0 24 + 14x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(12 + 7x + x2) = 0 Factor a trinomial. 2((4 + x)(3 + x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Solution
x = {-4, -3}
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