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Simplifying 12 + -2x = 8x(x + 4) Reorder the terms: 12 + -2x = 8x(4 + x) 12 + -2x = (4 * 8x + x * 8x) 12 + -2x = (32x + 8x2) Solving 12 + -2x = 32x + 8x2 Solving for variable 'x'. Combine like terms: -2x + -32x = -34x 12 + -34x + -8x2 = 32x + 8x2 + -32x + -8x2 Reorder the terms: 12 + -34x + -8x2 = 32x + -32x + 8x2 + -8x2 Combine like terms: 32x + -32x = 0 12 + -34x + -8x2 = 0 + 8x2 + -8x2 12 + -34x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 12 + -34x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(6 + -17x + -4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + -17x + -4x2)' equal to zero and attempt to solve: Simplifying 6 + -17x + -4x2 = 0 Solving 6 + -17x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.5 + 4.25x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 4.25x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 4.25x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 4.25x + x2 = 0 + 1.5 4.25x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 4.25x + x2 = 1.5 The x term is 4.25x. Take half its coefficient (2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. 4.25x + 4.515625 + x2 = 1.5 + 4.515625 Reorder the terms: 4.515625 + 4.25x + x2 = 1.5 + 4.515625 Combine like terms: 1.5 + 4.515625 = 6.015625 4.515625 + 4.25x + x2 = 6.015625 Factor a perfect square on the left side: (x + 2.125)(x + 2.125) = 6.015625 Calculate the square root of the right side: 2.452677109 Break this problem into two subproblems by setting (x + 2.125) equal to 2.452677109 and -2.452677109.Subproblem 1
x + 2.125 = 2.452677109 Simplifying x + 2.125 = 2.452677109 Reorder the terms: 2.125 + x = 2.452677109 Solving 2.125 + x = 2.452677109 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = 2.452677109 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = 2.452677109 + -2.125 x = 2.452677109 + -2.125 Combine like terms: 2.452677109 + -2.125 = 0.327677109 x = 0.327677109 Simplifying x = 0.327677109Subproblem 2
x + 2.125 = -2.452677109 Simplifying x + 2.125 = -2.452677109 Reorder the terms: 2.125 + x = -2.452677109 Solving 2.125 + x = -2.452677109 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = -2.452677109 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = -2.452677109 + -2.125 x = -2.452677109 + -2.125 Combine like terms: -2.452677109 + -2.125 = -4.577677109 x = -4.577677109 Simplifying x = -4.577677109Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.327677109, -4.577677109}Solution
x = {0.327677109, -4.577677109}
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