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Simplifying 10(x + -2)(30 + -1x) = 216 Reorder the terms: 10(-2 + x)(30 + -1x) = 216 Multiply (-2 + x) * (30 + -1x) 10(-2(30 + -1x) + x(30 + -1x)) = 216 10((30 * -2 + -1x * -2) + x(30 + -1x)) = 216 10((-60 + 2x) + x(30 + -1x)) = 216 10(-60 + 2x + (30 * x + -1x * x)) = 216 10(-60 + 2x + (30x + -1x2)) = 216 Combine like terms: 2x + 30x = 32x 10(-60 + 32x + -1x2) = 216 (-60 * 10 + 32x * 10 + -1x2 * 10) = 216 (-600 + 320x + -10x2) = 216 Solving -600 + 320x + -10x2 = 216 Solving for variable 'x'. Reorder the terms: -600 + -216 + 320x + -10x2 = 216 + -216 Combine like terms: -600 + -216 = -816 -816 + 320x + -10x2 = 216 + -216 Combine like terms: 216 + -216 = 0 -816 + 320x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-408 + 160x + -5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-408 + 160x + -5x2)' equal to zero and attempt to solve: Simplifying -408 + 160x + -5x2 = 0 Solving -408 + 160x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 81.6 + -32x + x2 = 0 Move the constant term to the right: Add '-81.6' to each side of the equation. 81.6 + -32x + -81.6 + x2 = 0 + -81.6 Reorder the terms: 81.6 + -81.6 + -32x + x2 = 0 + -81.6 Combine like terms: 81.6 + -81.6 = 0.0 0.0 + -32x + x2 = 0 + -81.6 -32x + x2 = 0 + -81.6 Combine like terms: 0 + -81.6 = -81.6 -32x + x2 = -81.6 The x term is -32x. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32x + 256 + x2 = -81.6 + 256 Reorder the terms: 256 + -32x + x2 = -81.6 + 256 Combine like terms: -81.6 + 256 = 174.4 256 + -32x + x2 = 174.4 Factor a perfect square on the left side: (x + -16)(x + -16) = 174.4 Calculate the square root of the right side: 13.206059215 Break this problem into two subproblems by setting (x + -16) equal to 13.206059215 and -13.206059215.Subproblem 1
x + -16 = 13.206059215 Simplifying x + -16 = 13.206059215 Reorder the terms: -16 + x = 13.206059215 Solving -16 + x = 13.206059215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 13.206059215 + 16 Combine like terms: -16 + 16 = 0 0 + x = 13.206059215 + 16 x = 13.206059215 + 16 Combine like terms: 13.206059215 + 16 = 29.206059215 x = 29.206059215 Simplifying x = 29.206059215Subproblem 2
x + -16 = -13.206059215 Simplifying x + -16 = -13.206059215 Reorder the terms: -16 + x = -13.206059215 Solving -16 + x = -13.206059215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = -13.206059215 + 16 Combine like terms: -16 + 16 = 0 0 + x = -13.206059215 + 16 x = -13.206059215 + 16 Combine like terms: -13.206059215 + 16 = 2.793940785 x = 2.793940785 Simplifying x = 2.793940785Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.206059215, 2.793940785}Solution
x = {29.206059215, 2.793940785}
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