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Simplifying 15x2 + -10x + -6 = 0 Reorder the terms: -6 + -10x + 15x2 = 0 Solving -6 + -10x + 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 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -0.6666666667x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -0.6666666667x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -0.6666666667x + x2 = 0 + 0.4 -0.6666666667x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -0.6666666667x + x2 = 0.4 The x term is -0.6666666667x. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667x + 0.1111111112 + x2 = 0.4 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = 0.4 + 0.1111111112 Combine like terms: 0.4 + 0.1111111112 = 0.5111111112 0.1111111112 + -0.6666666667x + x2 = 0.5111111112 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 0.5111111112 Calculate the square root of the right side: 0.714920353 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 0.714920353 and -0.714920353.Subproblem 1
x + -0.3333333334 = 0.714920353 Simplifying x + -0.3333333334 = 0.714920353 Reorder the terms: -0.3333333334 + x = 0.714920353 Solving -0.3333333334 + x = 0.714920353 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = 0.714920353 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 0.714920353 + 0.3333333334 x = 0.714920353 + 0.3333333334 Combine like terms: 0.714920353 + 0.3333333334 = 1.0482536864 x = 1.0482536864 Simplifying x = 1.0482536864Subproblem 2
x + -0.3333333334 = -0.714920353 Simplifying x + -0.3333333334 = -0.714920353 Reorder the terms: -0.3333333334 + x = -0.714920353 Solving -0.3333333334 + x = -0.714920353 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = -0.714920353 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -0.714920353 + 0.3333333334 x = -0.714920353 + 0.3333333334 Combine like terms: -0.714920353 + 0.3333333334 = -0.3815870196 x = -0.3815870196 Simplifying x = -0.3815870196Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0482536864, -0.3815870196}
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