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Simplifying 5x2 + 28x = 12x + -3x2 + 42 Reorder the terms: 28x + 5x2 = 12x + -3x2 + 42 Reorder the terms: 28x + 5x2 = 42 + 12x + -3x2 Solving 28x + 5x2 = 42 + 12x + -3x2 Solving for variable 'x'. Reorder the terms: -42 + 28x + -12x + 5x2 + 3x2 = 42 + 12x + -3x2 + -42 + -12x + 3x2 Combine like terms: 28x + -12x = 16x -42 + 16x + 5x2 + 3x2 = 42 + 12x + -3x2 + -42 + -12x + 3x2 Combine like terms: 5x2 + 3x2 = 8x2 -42 + 16x + 8x2 = 42 + 12x + -3x2 + -42 + -12x + 3x2 Reorder the terms: -42 + 16x + 8x2 = 42 + -42 + 12x + -12x + -3x2 + 3x2 Combine like terms: 42 + -42 = 0 -42 + 16x + 8x2 = 0 + 12x + -12x + -3x2 + 3x2 -42 + 16x + 8x2 = 12x + -12x + -3x2 + 3x2 Combine like terms: 12x + -12x = 0 -42 + 16x + 8x2 = 0 + -3x2 + 3x2 -42 + 16x + 8x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -42 + 16x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-21 + 8x + 4x2) = 0 Factor a trinomial. 2((-7 + -2x)(3 + -2x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -2x)' equal to zero and attempt to solve: Simplifying -7 + -2x = 0 Solving -7 + -2x = 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 + -2x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2x = 0 + 7 -2x = 0 + 7 Combine like terms: 0 + 7 = 7 -2x = 7 Divide each side by '-2'. x = -3.5 Simplifying x = -3.5Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {-3.5, 1.5}
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