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Simplifying 8x3 + 10x2 + -14x = 0 Reorder the terms: -14x + 10x2 + 8x3 = 0 Solving -14x + 10x2 + 8x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-7 + 5x + 4x2) = 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 '(-7 + 5x + 4x2)' equal to zero and attempt to solve: Simplifying -7 + 5x + 4x2 = 0 Solving -7 + 5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.75 + 1.25x + x2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + 1.25x + 1.75 + x2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + 1.25x + x2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + 1.25x + x2 = 0 + 1.75 1.25x + x2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 1.25x + x2 = 1.75 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 = 1.75 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 1.75 + 0.390625 Combine like terms: 1.75 + 0.390625 = 2.140625 0.390625 + 1.25x + x2 = 2.140625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 2.140625 Calculate the square root of the right side: 1.463087489 Break this problem into two subproblems by setting (x + 0.625) equal to 1.463087489 and -1.463087489.Subproblem 1
x + 0.625 = 1.463087489 Simplifying x + 0.625 = 1.463087489 Reorder the terms: 0.625 + x = 1.463087489 Solving 0.625 + x = 1.463087489 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 = 1.463087489 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 1.463087489 + -0.625 x = 1.463087489 + -0.625 Combine like terms: 1.463087489 + -0.625 = 0.838087489 x = 0.838087489 Simplifying x = 0.838087489Subproblem 2
x + 0.625 = -1.463087489 Simplifying x + 0.625 = -1.463087489 Reorder the terms: 0.625 + x = -1.463087489 Solving 0.625 + x = -1.463087489 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 = -1.463087489 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -1.463087489 + -0.625 x = -1.463087489 + -0.625 Combine like terms: -1.463087489 + -0.625 = -2.088087489 x = -2.088087489 Simplifying x = -2.088087489Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.838087489, -2.088087489}Solution
x = {0, 0.838087489, -2.088087489}
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