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Simplifying 4(5x + -9)(5x + -9) = 49 Reorder the terms: 4(-9 + 5x)(5x + -9) = 49 Reorder the terms: 4(-9 + 5x)(-9 + 5x) = 49 Multiply (-9 + 5x) * (-9 + 5x) 4(-9(-9 + 5x) + 5x * (-9 + 5x)) = 49 4((-9 * -9 + 5x * -9) + 5x * (-9 + 5x)) = 49 4((81 + -45x) + 5x * (-9 + 5x)) = 49 4(81 + -45x + (-9 * 5x + 5x * 5x)) = 49 4(81 + -45x + (-45x + 25x2)) = 49 Combine like terms: -45x + -45x = -90x 4(81 + -90x + 25x2) = 49 (81 * 4 + -90x * 4 + 25x2 * 4) = 49 (324 + -360x + 100x2) = 49 Solving 324 + -360x + 100x2 = 49 Solving for variable 'x'. Reorder the terms: 324 + -49 + -360x + 100x2 = 49 + -49 Combine like terms: 324 + -49 = 275 275 + -360x + 100x2 = 49 + -49 Combine like terms: 49 + -49 = 0 275 + -360x + 100x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(55 + -72x + 20x2) = 0 Factor a trinomial. 5((11 + -10x)(5 + -2x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(11 + -10x)' equal to zero and attempt to solve: Simplifying 11 + -10x = 0 Solving 11 + -10x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -10x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -10x = 0 + -11 -10x = 0 + -11 Combine like terms: 0 + -11 = -11 -10x = -11 Divide each side by '-10'. x = 1.1 Simplifying x = 1.1Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 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 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5Solution
x = {1.1, 2.5}
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