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Simplifying 15x2 + -20x + -6 = 0 Reorder the terms: -6 + -20x + 15x2 = 0 Solving -6 + -20x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.4 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -1.333333333x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -1.333333333x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -1.333333333x + x2 = 0 + 0.4 -1.333333333x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -1.333333333x + x2 = 0.4 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 = 0.4 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 0.4 + 0.4444444442 Combine like terms: 0.4 + 0.4444444442 = 0.8444444442 0.4444444442 + -1.333333333x + x2 = 0.8444444442 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 0.8444444442 Calculate the square root of the right side: 0.918936583 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 0.918936583 and -0.918936583.Subproblem 1
x + -0.6666666665 = 0.918936583 Simplifying x + -0.6666666665 = 0.918936583 Reorder the terms: -0.6666666665 + x = 0.918936583 Solving -0.6666666665 + x = 0.918936583 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 = 0.918936583 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 0.918936583 + 0.6666666665 x = 0.918936583 + 0.6666666665 Combine like terms: 0.918936583 + 0.6666666665 = 1.5856032495 x = 1.5856032495 Simplifying x = 1.5856032495Subproblem 2
x + -0.6666666665 = -0.918936583 Simplifying x + -0.6666666665 = -0.918936583 Reorder the terms: -0.6666666665 + x = -0.918936583 Solving -0.6666666665 + x = -0.918936583 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 = -0.918936583 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -0.918936583 + 0.6666666665 x = -0.918936583 + 0.6666666665 Combine like terms: -0.918936583 + 0.6666666665 = -0.2522699165 x = -0.2522699165 Simplifying x = -0.2522699165Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5856032495, -0.2522699165}
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