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Simplifying 50(x + 7) + 50(x + 7) = 8(x + 7)(x + -7) Reorder the terms: 50(7 + x) + 50(x + 7) = 8(x + 7)(x + -7) (7 * 50 + x * 50) + 50(x + 7) = 8(x + 7)(x + -7) (350 + 50x) + 50(x + 7) = 8(x + 7)(x + -7) Reorder the terms: 350 + 50x + 50(7 + x) = 8(x + 7)(x + -7) 350 + 50x + (7 * 50 + x * 50) = 8(x + 7)(x + -7) 350 + 50x + (350 + 50x) = 8(x + 7)(x + -7) Reorder the terms: 350 + 350 + 50x + 50x = 8(x + 7)(x + -7) Combine like terms: 350 + 350 = 700 700 + 50x + 50x = 8(x + 7)(x + -7) Combine like terms: 50x + 50x = 100x 700 + 100x = 8(x + 7)(x + -7) Reorder the terms: 700 + 100x = 8(7 + x)(x + -7) Reorder the terms: 700 + 100x = 8(7 + x)(-7 + x) Multiply (7 + x) * (-7 + x) 700 + 100x = 8(7(-7 + x) + x(-7 + x)) 700 + 100x = 8((-7 * 7 + x * 7) + x(-7 + x)) 700 + 100x = 8((-49 + 7x) + x(-7 + x)) 700 + 100x = 8(-49 + 7x + (-7 * x + x * x)) 700 + 100x = 8(-49 + 7x + (-7x + x2)) Combine like terms: 7x + -7x = 0 700 + 100x = 8(-49 + 0 + x2) 700 + 100x = 8(-49 + x2) 700 + 100x = (-49 * 8 + x2 * 8) 700 + 100x = (-392 + 8x2) Solving 700 + 100x = -392 + 8x2 Solving for variable 'x'. Reorder the terms: 700 + 392 + 100x + -8x2 = -392 + 8x2 + 392 + -8x2 Combine like terms: 700 + 392 = 1092 1092 + 100x + -8x2 = -392 + 8x2 + 392 + -8x2 Reorder the terms: 1092 + 100x + -8x2 = -392 + 392 + 8x2 + -8x2 Combine like terms: -392 + 392 = 0 1092 + 100x + -8x2 = 0 + 8x2 + -8x2 1092 + 100x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 1092 + 100x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(273 + 25x + -2x2) = 0 Factor a trinomial. 4((39 + -2x)(7 + x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(39 + -2x)' equal to zero and attempt to solve: Simplifying 39 + -2x = 0 Solving 39 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-39' to each side of the equation. 39 + -39 + -2x = 0 + -39 Combine like terms: 39 + -39 = 0 0 + -2x = 0 + -39 -2x = 0 + -39 Combine like terms: 0 + -39 = -39 -2x = -39 Divide each side by '-2'. x = 19.5 Simplifying x = 19.5Subproblem 2
Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 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 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Solution
x = {19.5, -7}
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