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Simplifying x3 + -12x2 = 16x Reorder the terms: -12x2 + x3 = 16x Solving -12x2 + x3 = 16x Solving for variable 'x'. Reorder the terms: -16x + -12x2 + x3 = 16x + -16x Combine like terms: 16x + -16x = 0 -16x + -12x2 + x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-16 + -12x + x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-16 + -12x + x2)' equal to zero and attempt to solve: Simplifying -16 + -12x + x2 = 0 Solving -16 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -12x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + -12x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -12x + x2 = 0 + 16 -12x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 -12x + x2 = 16 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 16 + 36 Reorder the terms: 36 + -12x + x2 = 16 + 36 Combine like terms: 16 + 36 = 52 36 + -12x + x2 = 52 Factor a perfect square on the left side: (x + -6)(x + -6) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (x + -6) equal to 7.211102551 and -7.211102551.Subproblem 1
x + -6 = 7.211102551 Simplifying x + -6 = 7.211102551 Reorder the terms: -6 + x = 7.211102551 Solving -6 + x = 7.211102551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 7.211102551 + 6 Combine like terms: -6 + 6 = 0 0 + x = 7.211102551 + 6 x = 7.211102551 + 6 Combine like terms: 7.211102551 + 6 = 13.211102551 x = 13.211102551 Simplifying x = 13.211102551Subproblem 2
x + -6 = -7.211102551 Simplifying x + -6 = -7.211102551 Reorder the terms: -6 + x = -7.211102551 Solving -6 + x = -7.211102551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -7.211102551 + 6 Combine like terms: -6 + 6 = 0 0 + x = -7.211102551 + 6 x = -7.211102551 + 6 Combine like terms: -7.211102551 + 6 = -1.211102551 x = -1.211102551 Simplifying x = -1.211102551Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.211102551, -1.211102551}Solution
x = {0, 13.211102551, -1.211102551}
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