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Simplifying 8x3 + 35x2 + -20x = 0 Reorder the terms: -20x + 35x2 + 8x3 = 0 Solving -20x + 35x2 + 8x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-20 + 35x + 8x2) = 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 '(-20 + 35x + 8x2)' equal to zero and attempt to solve: Simplifying -20 + 35x + 8x2 = 0 Solving -20 + 35x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.5 + 4.375x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 4.375x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 4.375x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 4.375x + x2 = 0 + 2.5 4.375x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 4.375x + x2 = 2.5 The x term is 4.375x. Take half its coefficient (2.1875). Square it (4.78515625) and add it to both sides. Add '4.78515625' to each side of the equation. 4.375x + 4.78515625 + x2 = 2.5 + 4.78515625 Reorder the terms: 4.78515625 + 4.375x + x2 = 2.5 + 4.78515625 Combine like terms: 2.5 + 4.78515625 = 7.28515625 4.78515625 + 4.375x + x2 = 7.28515625 Factor a perfect square on the left side: (x + 2.1875)(x + 2.1875) = 7.28515625 Calculate the square root of the right side: 2.69910286 Break this problem into two subproblems by setting (x + 2.1875) equal to 2.69910286 and -2.69910286.Subproblem 1
x + 2.1875 = 2.69910286 Simplifying x + 2.1875 = 2.69910286 Reorder the terms: 2.1875 + x = 2.69910286 Solving 2.1875 + x = 2.69910286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.1875' to each side of the equation. 2.1875 + -2.1875 + x = 2.69910286 + -2.1875 Combine like terms: 2.1875 + -2.1875 = 0.0000 0.0000 + x = 2.69910286 + -2.1875 x = 2.69910286 + -2.1875 Combine like terms: 2.69910286 + -2.1875 = 0.51160286 x = 0.51160286 Simplifying x = 0.51160286Subproblem 2
x + 2.1875 = -2.69910286 Simplifying x + 2.1875 = -2.69910286 Reorder the terms: 2.1875 + x = -2.69910286 Solving 2.1875 + x = -2.69910286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.1875' to each side of the equation. 2.1875 + -2.1875 + x = -2.69910286 + -2.1875 Combine like terms: 2.1875 + -2.1875 = 0.0000 0.0000 + x = -2.69910286 + -2.1875 x = -2.69910286 + -2.1875 Combine like terms: -2.69910286 + -2.1875 = -4.88660286 x = -4.88660286 Simplifying x = -4.88660286Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.51160286, -4.88660286}Solution
x = {0, 0.51160286, -4.88660286}
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