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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 = 0.0444444442 0.4444444442 + 1.333333333x + x2 = 0.0444444442 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 0.0444444442 Calculate the square root of the right side: 0.21081851 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 0.21081851 and -0.21081851.Subproblem 1
x + 0.6666666665 = 0.21081851 Simplifying x + 0.6666666665 = 0.21081851 Reorder the terms: 0.6666666665 + x = 0.21081851 Solving 0.6666666665 + x = 0.21081851 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 = 0.21081851 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 0.21081851 + -0.6666666665 x = 0.21081851 + -0.6666666665 Combine like terms: 0.21081851 + -0.6666666665 = -0.4558481565 x = -0.4558481565 Simplifying x = -0.4558481565Subproblem 2
x + 0.6666666665 = -0.21081851 Simplifying x + 0.6666666665 = -0.21081851 Reorder the terms: 0.6666666665 + x = -0.21081851 Solving 0.6666666665 + x = -0.21081851 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 = -0.21081851 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -0.21081851 + -0.6666666665 x = -0.21081851 + -0.6666666665 Combine like terms: -0.21081851 + -0.6666666665 = -0.8774851765 x = -0.8774851765 Simplifying x = -0.8774851765Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.4558481565, -0.8774851765}
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