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Simplifying 7x2 + -6x2 + 4x * 2x2 + -3x = 0 Reorder the terms for easier multiplication: 7x2 + -6x2 + 4 * 2x * x2 + -3x = 0 Multiply 4 * 2 7x2 + -6x2 + 8x * x2 + -3x = 0 Multiply x * x2 7x2 + -6x2 + 8x3 + -3x = 0 Reorder the terms: -3x + 7x2 + -6x2 + 8x3 = 0 Combine like terms: 7x2 + -6x2 = 1x2 -3x + 1x2 + 8x3 = 0 Solving -3x + 1x2 + 8x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-3 + x + 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 '(-3 + x + 8x2)' equal to zero and attempt to solve: Simplifying -3 + x + 8x2 = 0 Solving -3 + x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.375 + 0.125x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + 0.125x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + 0.125x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + 0.125x + x2 = 0 + 0.375 0.125x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 0.125x + x2 = 0.375 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.125x + 0.25 + x2 = 0.375 + 0.25 Reorder the terms: 0.25 + 0.125x + x2 = 0.375 + 0.25 Combine like terms: 0.375 + 0.25 = 0.625 0.25 + 0.125x + x2 = 0.625 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.625 Calculate the square root of the right side: 0.790569415 Break this problem into two subproblems by setting (x + 0.5) equal to 0.790569415 and -0.790569415.Subproblem 1
x + 0.5 = 0.790569415 Simplifying x + 0.5 = 0.790569415 Reorder the terms: 0.5 + x = 0.790569415 Solving 0.5 + x = 0.790569415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.790569415 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.790569415 + -0.5 x = 0.790569415 + -0.5 Combine like terms: 0.790569415 + -0.5 = 0.290569415 x = 0.290569415 Simplifying x = 0.290569415Subproblem 2
x + 0.5 = -0.790569415 Simplifying x + 0.5 = -0.790569415 Reorder the terms: 0.5 + x = -0.790569415 Solving 0.5 + x = -0.790569415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.790569415 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.790569415 + -0.5 x = -0.790569415 + -0.5 Combine like terms: -0.790569415 + -0.5 = -1.290569415 x = -1.290569415 Simplifying x = -1.290569415Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.290569415, -1.290569415}Solution
x = {0, 0.290569415, -1.290569415}
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