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Simplifying 2x3 + -32x2 + 26x = 0 Reorder the terms: 26x + -32x2 + 2x3 = 0 Solving 26x + -32x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(13 + -16x + x2) = 0 Ignore the factor 2.Subproblem 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 '(13 + -16x + x2)' equal to zero and attempt to solve: Simplifying 13 + -16x + x2 = 0 Solving 13 + -16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + -16x + -13 + x2 = 0 + -13 Reorder the terms: 13 + -13 + -16x + x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -16x + x2 = 0 + -13 -16x + x2 = 0 + -13 Combine like terms: 0 + -13 = -13 -16x + x2 = -13 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 = -13 + 64 Reorder the terms: 64 + -16x + x2 = -13 + 64 Combine like terms: -13 + 64 = 51 64 + -16x + x2 = 51 Factor a perfect square on the left side: (x + -8)(x + -8) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (x + -8) equal to 7.141428429 and -7.141428429.Subproblem 1
x + -8 = 7.141428429 Simplifying x + -8 = 7.141428429 Reorder the terms: -8 + x = 7.141428429 Solving -8 + x = 7.141428429 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 = 7.141428429 + 8 Combine like terms: -8 + 8 = 0 0 + x = 7.141428429 + 8 x = 7.141428429 + 8 Combine like terms: 7.141428429 + 8 = 15.141428429 x = 15.141428429 Simplifying x = 15.141428429Subproblem 2
x + -8 = -7.141428429 Simplifying x + -8 = -7.141428429 Reorder the terms: -8 + x = -7.141428429 Solving -8 + x = -7.141428429 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 = -7.141428429 + 8 Combine like terms: -8 + 8 = 0 0 + x = -7.141428429 + 8 x = -7.141428429 + 8 Combine like terms: -7.141428429 + 8 = 0.858571571 x = 0.858571571 Simplifying x = 0.858571571Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.141428429, 0.858571571}Solution
x = {0, 15.141428429, 0.858571571}
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