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Simplifying (x * x) + (x + 7)(x + 7) = 1429 Multiply x * x (x2) + (x + 7)(x + 7) = 1429 x2 + (x + 7)(x + 7) = 1429 Reorder the terms: x2 + (7 + x)(x + 7) = 1429 Reorder the terms: x2 + (7 + x)(7 + x) = 1429 Multiply (7 + x) * (7 + x) x2 + (7(7 + x) + x(7 + x)) = 1429 x2 + ((7 * 7 + x * 7) + x(7 + x)) = 1429 x2 + ((49 + 7x) + x(7 + x)) = 1429 x2 + (49 + 7x + (7 * x + x * x)) = 1429 x2 + (49 + 7x + (7x + x2)) = 1429 Combine like terms: 7x + 7x = 14x x2 + (49 + 14x + x2) = 1429 Reorder the terms: 49 + 14x + x2 + x2 = 1429 Combine like terms: x2 + x2 = 2x2 49 + 14x + 2x2 = 1429 Solving 49 + 14x + 2x2 = 1429 Solving for variable 'x'. Reorder the terms: 49 + -1429 + 14x + 2x2 = 1429 + -1429 Combine like terms: 49 + -1429 = -1380 -1380 + 14x + 2x2 = 1429 + -1429 Combine like terms: 1429 + -1429 = 0 -1380 + 14x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-690 + 7x + x2) = 0 Factor a trinomial. 2((-30 + -1x)(23 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-30 + -1x)' equal to zero and attempt to solve: Simplifying -30 + -1x = 0 Solving -30 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + -1x = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -1x = 0 + 30 -1x = 0 + 30 Combine like terms: 0 + 30 = 30 -1x = 30 Divide each side by '-1'. x = -30 Simplifying x = -30Subproblem 2
Set the factor '(23 + -1x)' equal to zero and attempt to solve: Simplifying 23 + -1x = 0 Solving 23 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + -1x = 0 + -23 Combine like terms: 23 + -23 = 0 0 + -1x = 0 + -23 -1x = 0 + -23 Combine like terms: 0 + -23 = -23 -1x = -23 Divide each side by '-1'. x = 23 Simplifying x = 23Solution
x = {-30, 23}
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