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Simplifying 2x3 + -8x2 + -63x = 0 Reorder the terms: -63x + -8x2 + 2x3 = 0 Solving -63x + -8x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-63 + -8x + 2x2) = 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 '(-63 + -8x + 2x2)' equal to zero and attempt to solve: Simplifying -63 + -8x + 2x2 = 0 Solving -63 + -8x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -31.5 + -4x + x2 = 0 Move the constant term to the right: Add '31.5' to each side of the equation. -31.5 + -4x + 31.5 + x2 = 0 + 31.5 Reorder the terms: -31.5 + 31.5 + -4x + x2 = 0 + 31.5 Combine like terms: -31.5 + 31.5 = 0.0 0.0 + -4x + x2 = 0 + 31.5 -4x + x2 = 0 + 31.5 Combine like terms: 0 + 31.5 = 31.5 -4x + x2 = 31.5 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 31.5 + 4 Reorder the terms: 4 + -4x + x2 = 31.5 + 4 Combine like terms: 31.5 + 4 = 35.5 4 + -4x + x2 = 35.5 Factor a perfect square on the left side: (x + -2)(x + -2) = 35.5 Calculate the square root of the right side: 5.958187644 Break this problem into two subproblems by setting (x + -2) equal to 5.958187644 and -5.958187644.Subproblem 1
x + -2 = 5.958187644 Simplifying x + -2 = 5.958187644 Reorder the terms: -2 + x = 5.958187644 Solving -2 + x = 5.958187644 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 5.958187644 + 2 Combine like terms: -2 + 2 = 0 0 + x = 5.958187644 + 2 x = 5.958187644 + 2 Combine like terms: 5.958187644 + 2 = 7.958187644 x = 7.958187644 Simplifying x = 7.958187644Subproblem 2
x + -2 = -5.958187644 Simplifying x + -2 = -5.958187644 Reorder the terms: -2 + x = -5.958187644 Solving -2 + x = -5.958187644 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -5.958187644 + 2 Combine like terms: -2 + 2 = 0 0 + x = -5.958187644 + 2 x = -5.958187644 + 2 Combine like terms: -5.958187644 + 2 = -3.958187644 x = -3.958187644 Simplifying x = -3.958187644Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.958187644, -3.958187644}Solution
x = {0, 7.958187644, -3.958187644}
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