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Simplifying 8x2 + 10x = 46 Reorder the terms: 10x + 8x2 = 46 Solving 10x + 8x2 = 46 Solving for variable 'x'. Reorder the terms: -46 + 10x + 8x2 = 46 + -46 Combine like terms: 46 + -46 = 0 -46 + 10x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-23 + 5x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-23 + 5x + 4x2)' equal to zero and attempt to solve: Simplifying -23 + 5x + 4x2 = 0 Solving -23 + 5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5.75 + 1.25x + x2 = 0 Move the constant term to the right: Add '5.75' to each side of the equation. -5.75 + 1.25x + 5.75 + x2 = 0 + 5.75 Reorder the terms: -5.75 + 5.75 + 1.25x + x2 = 0 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + 1.25x + x2 = 0 + 5.75 1.25x + x2 = 0 + 5.75 Combine like terms: 0 + 5.75 = 5.75 1.25x + x2 = 5.75 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 = 5.75 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 5.75 + 0.390625 Combine like terms: 5.75 + 0.390625 = 6.140625 0.390625 + 1.25x + x2 = 6.140625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 6.140625 Calculate the square root of the right side: 2.47802845 Break this problem into two subproblems by setting (x + 0.625) equal to 2.47802845 and -2.47802845.Subproblem 1
x + 0.625 = 2.47802845 Simplifying x + 0.625 = 2.47802845 Reorder the terms: 0.625 + x = 2.47802845 Solving 0.625 + x = 2.47802845 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 = 2.47802845 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 2.47802845 + -0.625 x = 2.47802845 + -0.625 Combine like terms: 2.47802845 + -0.625 = 1.85302845 x = 1.85302845 Simplifying x = 1.85302845Subproblem 2
x + 0.625 = -2.47802845 Simplifying x + 0.625 = -2.47802845 Reorder the terms: 0.625 + x = -2.47802845 Solving 0.625 + x = -2.47802845 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 = -2.47802845 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -2.47802845 + -0.625 x = -2.47802845 + -0.625 Combine like terms: -2.47802845 + -0.625 = -3.10302845 x = -3.10302845 Simplifying x = -3.10302845Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.85302845, -3.10302845}Solution
x = {1.85302845, -3.10302845}
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