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Simplifying 12 + -1(2x + -5)(2x + -5) = 3x Reorder the terms: 12 + -1(-5 + 2x)(2x + -5) = 3x Reorder the terms: 12 + -1(-5 + 2x)(-5 + 2x) = 3x Multiply (-5 + 2x) * (-5 + 2x) 12 + -1(-5(-5 + 2x) + 2x * (-5 + 2x)) = 3x 12 + -1((-5 * -5 + 2x * -5) + 2x * (-5 + 2x)) = 3x 12 + -1((25 + -10x) + 2x * (-5 + 2x)) = 3x 12 + -1(25 + -10x + (-5 * 2x + 2x * 2x)) = 3x 12 + -1(25 + -10x + (-10x + 4x2)) = 3x Combine like terms: -10x + -10x = -20x 12 + -1(25 + -20x + 4x2) = 3x 12 + (25 * -1 + -20x * -1 + 4x2 * -1) = 3x 12 + (-25 + 20x + -4x2) = 3x Combine like terms: 12 + -25 = -13 -13 + 20x + -4x2 = 3x Solving -13 + 20x + -4x2 = 3x Solving for variable 'x'. Reorder the terms: -13 + 20x + -3x + -4x2 = 3x + -3x Combine like terms: 20x + -3x = 17x -13 + 17x + -4x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -13 + 17x + -4x2 = 0 Factor a trinomial. (-13 + 4x)(1 + -1x) = 0Subproblem 1
Set the factor '(-13 + 4x)' equal to zero and attempt to solve: Simplifying -13 + 4x = 0 Solving -13 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + 4x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 4x = 0 + 13 4x = 0 + 13 Combine like terms: 0 + 13 = 13 4x = 13 Divide each side by '4'. x = 3.25 Simplifying x = 3.25Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {3.25, 1}
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