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Simplifying 12x2 + 16x + -15 = 0 Reorder the terms: -15 + 16x + 12x2 = 0 Solving -15 + 16x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -1.25 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 1.333333333x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 1.333333333x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 1.333333333x + x2 = 0 + 1.25 1.333333333x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 1.333333333x + x2 = 1.25 The x term is 1.333333333x. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333x + 0.4444444442 + x2 = 1.25 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 1.25 + 0.4444444442 Combine like terms: 1.25 + 0.4444444442 = 1.6944444442 0.4444444442 + 1.333333333x + x2 = 1.6944444442 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 1.6944444442 Calculate the square root of the right side: 1.301708279 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 1.301708279 and -1.301708279.Subproblem 1
x + 0.6666666665 = 1.301708279 Simplifying x + 0.6666666665 = 1.301708279 Reorder the terms: 0.6666666665 + x = 1.301708279 Solving 0.6666666665 + x = 1.301708279 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = 1.301708279 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 1.301708279 + -0.6666666665 x = 1.301708279 + -0.6666666665 Combine like terms: 1.301708279 + -0.6666666665 = 0.6350416125 x = 0.6350416125 Simplifying x = 0.6350416125Subproblem 2
x + 0.6666666665 = -1.301708279 Simplifying x + 0.6666666665 = -1.301708279 Reorder the terms: 0.6666666665 + x = -1.301708279 Solving 0.6666666665 + x = -1.301708279 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = -1.301708279 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -1.301708279 + -0.6666666665 x = -1.301708279 + -0.6666666665 Combine like terms: -1.301708279 + -0.6666666665 = -1.9683749455 x = -1.9683749455 Simplifying x = -1.9683749455Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6350416125, -1.9683749455}
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