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Simplifying 4x3 + -5x2 + -8x + 10 = 10 Reorder the terms: 10 + -8x + -5x2 + 4x3 = 10 Add '-10' to each side of the equation. 10 + -8x + -5x2 + -10 + 4x3 = 10 + -10 Reorder the terms: 10 + -10 + -8x + -5x2 + 4x3 = 10 + -10 Combine like terms: 10 + -10 = 0 0 + -8x + -5x2 + 4x3 = 10 + -10 -8x + -5x2 + 4x3 = 10 + -10 Combine like terms: 10 + -10 = 0 -8x + -5x2 + 4x3 = 0 Solving -8x + -5x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-8 + -5x + 4x2) = 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 '(-8 + -5x + 4x2)' equal to zero and attempt to solve: Simplifying -8 + -5x + 4x2 = 0 Solving -8 + -5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2 + -1.25x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -1.25x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -1.25x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1.25x + x2 = 0 + 2 -1.25x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -1.25x + x2 = 2 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = 2 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 2 + 0.390625 Combine like terms: 2 + 0.390625 = 2.390625 0.390625 + -1.25x + x2 = 2.390625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 2.390625 Calculate the square root of the right side: 1.54616461 Break this problem into two subproblems by setting (x + -0.625) equal to 1.54616461 and -1.54616461.Subproblem 1
x + -0.625 = 1.54616461 Simplifying x + -0.625 = 1.54616461 Reorder the terms: -0.625 + x = 1.54616461 Solving -0.625 + x = 1.54616461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 1.54616461 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 1.54616461 + 0.625 x = 1.54616461 + 0.625 Combine like terms: 1.54616461 + 0.625 = 2.17116461 x = 2.17116461 Simplifying x = 2.17116461Subproblem 2
x + -0.625 = -1.54616461 Simplifying x + -0.625 = -1.54616461 Reorder the terms: -0.625 + x = -1.54616461 Solving -0.625 + x = -1.54616461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -1.54616461 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -1.54616461 + 0.625 x = -1.54616461 + 0.625 Combine like terms: -1.54616461 + 0.625 = -0.92116461 x = -0.92116461 Simplifying x = -0.92116461Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.17116461, -0.92116461}Solution
x = {0, 2.17116461, -0.92116461}
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