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Simplifying 4x2 + 10x + -6 = 186 Reorder the terms: -6 + 10x + 4x2 = 186 Solving -6 + 10x + 4x2 = 186 Solving for variable 'x'. Reorder the terms: -6 + -186 + 10x + 4x2 = 186 + -186 Combine like terms: -6 + -186 = -192 -192 + 10x + 4x2 = 186 + -186 Combine like terms: 186 + -186 = 0 -192 + 10x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-96 + 5x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-96 + 5x + 2x2)' equal to zero and attempt to solve: Simplifying -96 + 5x + 2x2 = 0 Solving -96 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -48 + 2.5x + x2 = 0 Move the constant term to the right: Add '48' to each side of the equation. -48 + 2.5x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + 2.5x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 2.5x + x2 = 0 + 48 2.5x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 2.5x + x2 = 48 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 48 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 48 + 1.5625 Combine like terms: 48 + 1.5625 = 49.5625 1.5625 + 2.5x + x2 = 49.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 49.5625 Calculate the square root of the right side: 7.04006392 Break this problem into two subproblems by setting (x + 1.25) equal to 7.04006392 and -7.04006392.Subproblem 1
x + 1.25 = 7.04006392 Simplifying x + 1.25 = 7.04006392 Reorder the terms: 1.25 + x = 7.04006392 Solving 1.25 + x = 7.04006392 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 7.04006392 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 7.04006392 + -1.25 x = 7.04006392 + -1.25 Combine like terms: 7.04006392 + -1.25 = 5.79006392 x = 5.79006392 Simplifying x = 5.79006392Subproblem 2
x + 1.25 = -7.04006392 Simplifying x + 1.25 = -7.04006392 Reorder the terms: 1.25 + x = -7.04006392 Solving 1.25 + x = -7.04006392 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -7.04006392 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -7.04006392 + -1.25 x = -7.04006392 + -1.25 Combine like terms: -7.04006392 + -1.25 = -8.29006392 x = -8.29006392 Simplifying x = -8.29006392Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.79006392, -8.29006392}Solution
x = {5.79006392, -8.29006392}
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