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Simplifying -3x2 + 48x = 87 Reorder the terms: 48x + -3x2 = 87 Solving 48x + -3x2 = 87 Solving for variable 'x'. Reorder the terms: -87 + 48x + -3x2 = 87 + -87 Combine like terms: 87 + -87 = 0 -87 + 48x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-29 + 16x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-29 + 16x + -1x2)' equal to zero and attempt to solve: Simplifying -29 + 16x + -1x2 = 0 Solving -29 + 16x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 29 + -16x + x2 = 0 Move the constant term to the right: Add '-29' to each side of the equation. 29 + -16x + -29 + x2 = 0 + -29 Reorder the terms: 29 + -29 + -16x + x2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + -16x + x2 = 0 + -29 -16x + x2 = 0 + -29 Combine like terms: 0 + -29 = -29 -16x + x2 = -29 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = -29 + 64 Reorder the terms: 64 + -16x + x2 = -29 + 64 Combine like terms: -29 + 64 = 35 64 + -16x + x2 = 35 Factor a perfect square on the left side: (x + -8)(x + -8) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (x + -8) equal to 5.916079783 and -5.916079783.Subproblem 1
x + -8 = 5.916079783 Simplifying x + -8 = 5.916079783 Reorder the terms: -8 + x = 5.916079783 Solving -8 + x = 5.916079783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 5.916079783 + 8 Combine like terms: -8 + 8 = 0 0 + x = 5.916079783 + 8 x = 5.916079783 + 8 Combine like terms: 5.916079783 + 8 = 13.916079783 x = 13.916079783 Simplifying x = 13.916079783Subproblem 2
x + -8 = -5.916079783 Simplifying x + -8 = -5.916079783 Reorder the terms: -8 + x = -5.916079783 Solving -8 + x = -5.916079783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -5.916079783 + 8 Combine like terms: -8 + 8 = 0 0 + x = -5.916079783 + 8 x = -5.916079783 + 8 Combine like terms: -5.916079783 + 8 = 2.083920217 x = 2.083920217 Simplifying x = 2.083920217Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.916079783, 2.083920217}Solution
x = {13.916079783, 2.083920217}
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