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Simplifying 15x2 + 34x + -6 = 0 Reorder the terms: -6 + 34x + 15x2 = 0 Solving -6 + 34x + 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 + 2.266666667x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 2.266666667x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 2.266666667x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 2.266666667x + x2 = 0 + 0.4 2.266666667x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 2.266666667x + x2 = 0.4 The x term is 2.266666667x. Take half its coefficient (1.133333334). Square it (1.284444446) and add it to both sides. Add '1.284444446' to each side of the equation. 2.266666667x + 1.284444446 + x2 = 0.4 + 1.284444446 Reorder the terms: 1.284444446 + 2.266666667x + x2 = 0.4 + 1.284444446 Combine like terms: 0.4 + 1.284444446 = 1.684444446 1.284444446 + 2.266666667x + x2 = 1.684444446 Factor a perfect square on the left side: (x + 1.133333334)(x + 1.133333334) = 1.684444446 Calculate the square root of the right side: 1.29786149 Break this problem into two subproblems by setting (x + 1.133333334) equal to 1.29786149 and -1.29786149.Subproblem 1
x + 1.133333334 = 1.29786149 Simplifying x + 1.133333334 = 1.29786149 Reorder the terms: 1.133333334 + x = 1.29786149 Solving 1.133333334 + x = 1.29786149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.133333334' to each side of the equation. 1.133333334 + -1.133333334 + x = 1.29786149 + -1.133333334 Combine like terms: 1.133333334 + -1.133333334 = 0.000000000 0.000000000 + x = 1.29786149 + -1.133333334 x = 1.29786149 + -1.133333334 Combine like terms: 1.29786149 + -1.133333334 = 0.164528156 x = 0.164528156 Simplifying x = 0.164528156Subproblem 2
x + 1.133333334 = -1.29786149 Simplifying x + 1.133333334 = -1.29786149 Reorder the terms: 1.133333334 + x = -1.29786149 Solving 1.133333334 + x = -1.29786149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.133333334' to each side of the equation. 1.133333334 + -1.133333334 + x = -1.29786149 + -1.133333334 Combine like terms: 1.133333334 + -1.133333334 = 0.000000000 0.000000000 + x = -1.29786149 + -1.133333334 x = -1.29786149 + -1.133333334 Combine like terms: -1.29786149 + -1.133333334 = -2.431194824 x = -2.431194824 Simplifying x = -2.431194824Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.164528156, -2.431194824}
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