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Simplifying 0 = 15x2 + -94x + 12 Reorder the terms: 0 = 12 + -94x + 15x2 Solving 0 = 12 + -94x + 15x2 Solving for variable 'x'. Combine like terms: 0 + -12 = -12 -12 + 94x + -15x2 = 12 + -94x + 15x2 + -12 + 94x + -15x2 Reorder the terms: -12 + 94x + -15x2 = 12 + -12 + -94x + 94x + 15x2 + -15x2 Combine like terms: 12 + -12 = 0 -12 + 94x + -15x2 = 0 + -94x + 94x + 15x2 + -15x2 -12 + 94x + -15x2 = -94x + 94x + 15x2 + -15x2 Combine like terms: -94x + 94x = 0 -12 + 94x + -15x2 = 0 + 15x2 + -15x2 -12 + 94x + -15x2 = 15x2 + -15x2 Combine like terms: 15x2 + -15x2 = 0 -12 + 94x + -15x2 = 0 Begin completing the square. Divide all terms by -15 the coefficient of the squared term: Divide each side by '-15'. 0.8 + -6.266666667x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + -6.266666667x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + -6.266666667x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + -6.266666667x + x2 = 0 + -0.8 -6.266666667x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 -6.266666667x + x2 = -0.8 The x term is -6.266666667x. Take half its coefficient (-3.133333334). Square it (9.817777782) and add it to both sides. Add '9.817777782' to each side of the equation. -6.266666667x + 9.817777782 + x2 = -0.8 + 9.817777782 Reorder the terms: 9.817777782 + -6.266666667x + x2 = -0.8 + 9.817777782 Combine like terms: -0.8 + 9.817777782 = 9.017777782 9.817777782 + -6.266666667x + x2 = 9.017777782 Factor a perfect square on the left side: (x + -3.133333334)(x + -3.133333334) = 9.017777782 Calculate the square root of the right side: 3.002961502 Break this problem into two subproblems by setting (x + -3.133333334) equal to 3.002961502 and -3.002961502.Subproblem 1
x + -3.133333334 = 3.002961502 Simplifying x + -3.133333334 = 3.002961502 Reorder the terms: -3.133333334 + x = 3.002961502 Solving -3.133333334 + x = 3.002961502 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.133333334' to each side of the equation. -3.133333334 + 3.133333334 + x = 3.002961502 + 3.133333334 Combine like terms: -3.133333334 + 3.133333334 = 0.000000000 0.000000000 + x = 3.002961502 + 3.133333334 x = 3.002961502 + 3.133333334 Combine like terms: 3.002961502 + 3.133333334 = 6.136294836 x = 6.136294836 Simplifying x = 6.136294836Subproblem 2
x + -3.133333334 = -3.002961502 Simplifying x + -3.133333334 = -3.002961502 Reorder the terms: -3.133333334 + x = -3.002961502 Solving -3.133333334 + x = -3.002961502 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.133333334' to each side of the equation. -3.133333334 + 3.133333334 + x = -3.002961502 + 3.133333334 Combine like terms: -3.133333334 + 3.133333334 = 0.000000000 0.000000000 + x = -3.002961502 + 3.133333334 x = -3.002961502 + 3.133333334 Combine like terms: -3.002961502 + 3.133333334 = 0.130371832 x = 0.130371832 Simplifying x = 0.130371832Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.136294836, 0.130371832}
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