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Simplifying ((2x + -9)(2x + -9)) + (3x * 3x) = ((5x + -21)(5x + -21)) Reorder the terms: ((-9 + 2x)(2x + -9)) + (3x * 3x) = ((5x + -21)(5x + -21)) Reorder the terms: ((-9 + 2x)(-9 + 2x)) + (3x * 3x) = ((5x + -21)(5x + -21)) Multiply (-9 + 2x) * (-9 + 2x) ((-9(-9 + 2x) + 2x * (-9 + 2x))) + (3x * 3x) = ((5x + -21)(5x + -21)) (((-9 * -9 + 2x * -9) + 2x * (-9 + 2x))) + (3x * 3x) = ((5x + -21)(5x + -21)) (((81 + -18x) + 2x * (-9 + 2x))) + (3x * 3x) = ((5x + -21)(5x + -21)) ((81 + -18x + (-9 * 2x + 2x * 2x))) + (3x * 3x) = ((5x + -21)(5x + -21)) ((81 + -18x + (-18x + 4x2))) + (3x * 3x) = ((5x + -21)(5x + -21)) Combine like terms: -18x + -18x = -36x ((81 + -36x + 4x2)) + (3x * 3x) = ((5x + -21)(5x + -21)) (81 + -36x + 4x2) + (3x * 3x) = ((5x + -21)(5x + -21)) Remove parenthesis around (81 + -36x + 4x2) 81 + -36x + 4x2 + (3x * 3x) = ((5x + -21)(5x + -21)) Reorder the terms for easier multiplication: 81 + -36x + 4x2 + (3 * 3x * x) = ((5x + -21)(5x + -21)) Multiply 3 * 3 81 + -36x + 4x2 + (9x * x) = ((5x + -21)(5x + -21)) Multiply x * x 81 + -36x + 4x2 + (9x2) = ((5x + -21)(5x + -21)) Combine like terms: 4x2 + (9x2) = 13x2 81 + -36x + 13x2 = ((5x + -21)(5x + -21)) Reorder the terms: 81 + -36x + 13x2 = ((-21 + 5x)(5x + -21)) Reorder the terms: 81 + -36x + 13x2 = ((-21 + 5x)(-21 + 5x)) Multiply (-21 + 5x) * (-21 + 5x) 81 + -36x + 13x2 = ((-21(-21 + 5x) + 5x * (-21 + 5x))) 81 + -36x + 13x2 = (((-21 * -21 + 5x * -21) + 5x * (-21 + 5x))) 81 + -36x + 13x2 = (((441 + -105x) + 5x * (-21 + 5x))) 81 + -36x + 13x2 = ((441 + -105x + (-21 * 5x + 5x * 5x))) 81 + -36x + 13x2 = ((441 + -105x + (-105x + 25x2))) Combine like terms: -105x + -105x = -210x 81 + -36x + 13x2 = ((441 + -210x + 25x2)) 81 + -36x + 13x2 = (441 + -210x + 25x2) Remove parenthesis around (441 + -210x + 25x2) 81 + -36x + 13x2 = 441 + -210x + 25x2 Solving 81 + -36x + 13x2 = 441 + -210x + 25x2 Solving for variable 'x'. Reorder the terms: 81 + -441 + -36x + 210x + 13x2 + -25x2 = 441 + -210x + 25x2 + -441 + 210x + -25x2 Combine like terms: 81 + -441 = -360 -360 + -36x + 210x + 13x2 + -25x2 = 441 + -210x + 25x2 + -441 + 210x + -25x2 Combine like terms: -36x + 210x = 174x -360 + 174x + 13x2 + -25x2 = 441 + -210x + 25x2 + -441 + 210x + -25x2 Combine like terms: 13x2 + -25x2 = -12x2 -360 + 174x + -12x2 = 441 + -210x + 25x2 + -441 + 210x + -25x2 Reorder the terms: -360 + 174x + -12x2 = 441 + -441 + -210x + 210x + 25x2 + -25x2 Combine like terms: 441 + -441 = 0 -360 + 174x + -12x2 = 0 + -210x + 210x + 25x2 + -25x2 -360 + 174x + -12x2 = -210x + 210x + 25x2 + -25x2 Combine like terms: -210x + 210x = 0 -360 + 174x + -12x2 = 0 + 25x2 + -25x2 -360 + 174x + -12x2 = 25x2 + -25x2 Combine like terms: 25x2 + -25x2 = 0 -360 + 174x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-60 + 29x + -2x2) = 0 Factor a trinomial. 6((-12 + x)(5 + -2x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-12 + x)' equal to zero and attempt to solve: Simplifying -12 + x = 0 Solving -12 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + x = 0 + 12 x = 0 + 12 Combine like terms: 0 + 12 = 12 x = 12 Simplifying x = 12Subproblem 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 = {12, 2.5}
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