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Simplifying 2x3 + -4x2 + -96x = 8x2 Reorder the terms: -96x + -4x2 + 2x3 = 8x2 Solving -96x + -4x2 + 2x3 = 8x2 Solving for variable 'x'. Reorder the terms: -96x + -4x2 + -8x2 + 2x3 = 8x2 + -8x2 Combine like terms: -4x2 + -8x2 = -12x2 -96x + -12x2 + 2x3 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -96x + -12x2 + 2x3 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(-48 + -6x + 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 '(-48 + -6x + x2)' equal to zero and attempt to solve: Simplifying -48 + -6x + x2 = 0 Solving -48 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + -6x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + -6x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -6x + x2 = 0 + 48 -6x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 -6x + x2 = 48 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 48 + 9 Reorder the terms: 9 + -6x + x2 = 48 + 9 Combine like terms: 48 + 9 = 57 9 + -6x + x2 = 57 Factor a perfect square on the left side: (x + -3)(x + -3) = 57 Calculate the square root of the right side: 7.549834435 Break this problem into two subproblems by setting (x + -3) equal to 7.549834435 and -7.549834435.Subproblem 1
x + -3 = 7.549834435 Simplifying x + -3 = 7.549834435 Reorder the terms: -3 + x = 7.549834435 Solving -3 + x = 7.549834435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 7.549834435 + 3 Combine like terms: -3 + 3 = 0 0 + x = 7.549834435 + 3 x = 7.549834435 + 3 Combine like terms: 7.549834435 + 3 = 10.549834435 x = 10.549834435 Simplifying x = 10.549834435Subproblem 2
x + -3 = -7.549834435 Simplifying x + -3 = -7.549834435 Reorder the terms: -3 + x = -7.549834435 Solving -3 + x = -7.549834435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -7.549834435 + 3 Combine like terms: -3 + 3 = 0 0 + x = -7.549834435 + 3 x = -7.549834435 + 3 Combine like terms: -7.549834435 + 3 = -4.549834435 x = -4.549834435 Simplifying x = -4.549834435Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.549834435, -4.549834435}Solution
x = {0, 10.549834435, -4.549834435}
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