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Simplifying 8x2 + 6x = 112 Reorder the terms: 6x + 8x2 = 112 Solving 6x + 8x2 = 112 Solving for variable 'x'. Reorder the terms: -112 + 6x + 8x2 = 112 + -112 Combine like terms: 112 + -112 = 0 -112 + 6x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-56 + 3x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-56 + 3x + 4x2)' equal to zero and attempt to solve: Simplifying -56 + 3x + 4x2 = 0 Solving -56 + 3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -14 + 0.75x + x2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + 0.75x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + 0.75x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 0.75x + x2 = 0 + 14 0.75x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 0.75x + x2 = 14 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 14 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 14 + 0.140625 Combine like terms: 14 + 0.140625 = 14.140625 0.140625 + 0.75x + x2 = 14.140625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 14.140625 Calculate the square root of the right side: 3.760402239 Break this problem into two subproblems by setting (x + 0.375) equal to 3.760402239 and -3.760402239.Subproblem 1
x + 0.375 = 3.760402239 Simplifying x + 0.375 = 3.760402239 Reorder the terms: 0.375 + x = 3.760402239 Solving 0.375 + x = 3.760402239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 3.760402239 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 3.760402239 + -0.375 x = 3.760402239 + -0.375 Combine like terms: 3.760402239 + -0.375 = 3.385402239 x = 3.385402239 Simplifying x = 3.385402239Subproblem 2
x + 0.375 = -3.760402239 Simplifying x + 0.375 = -3.760402239 Reorder the terms: 0.375 + x = -3.760402239 Solving 0.375 + x = -3.760402239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -3.760402239 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -3.760402239 + -0.375 x = -3.760402239 + -0.375 Combine like terms: -3.760402239 + -0.375 = -4.135402239 x = -4.135402239 Simplifying x = -4.135402239Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.385402239, -4.135402239}Solution
x = {3.385402239, -4.135402239}
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