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Simplifying 15x2 + -16x + -8 = 0 Reorder the terms: -8 + -16x + 15x2 = 0 Solving -8 + -16x + 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'. -0.5333333333 + -1.066666667x + x2 = 0 Move the constant term to the right: Add '0.5333333333' to each side of the equation. -0.5333333333 + -1.066666667x + 0.5333333333 + x2 = 0 + 0.5333333333 Reorder the terms: -0.5333333333 + 0.5333333333 + -1.066666667x + x2 = 0 + 0.5333333333 Combine like terms: -0.5333333333 + 0.5333333333 = 0.0000000000 0.0000000000 + -1.066666667x + x2 = 0 + 0.5333333333 -1.066666667x + x2 = 0 + 0.5333333333 Combine like terms: 0 + 0.5333333333 = 0.5333333333 -1.066666667x + x2 = 0.5333333333 The x term is -1.066666667x. Take half its coefficient (-0.5333333335). Square it (0.2844444446) and add it to both sides. Add '0.2844444446' to each side of the equation. -1.066666667x + 0.2844444446 + x2 = 0.5333333333 + 0.2844444446 Reorder the terms: 0.2844444446 + -1.066666667x + x2 = 0.5333333333 + 0.2844444446 Combine like terms: 0.5333333333 + 0.2844444446 = 0.8177777779 0.2844444446 + -1.066666667x + x2 = 0.8177777779 Factor a perfect square on the left side: (x + -0.5333333335)(x + -0.5333333335) = 0.8177777779 Calculate the square root of the right side: 0.904310664 Break this problem into two subproblems by setting (x + -0.5333333335) equal to 0.904310664 and -0.904310664.Subproblem 1
x + -0.5333333335 = 0.904310664 Simplifying x + -0.5333333335 = 0.904310664 Reorder the terms: -0.5333333335 + x = 0.904310664 Solving -0.5333333335 + x = 0.904310664 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5333333335' to each side of the equation. -0.5333333335 + 0.5333333335 + x = 0.904310664 + 0.5333333335 Combine like terms: -0.5333333335 + 0.5333333335 = 0.0000000000 0.0000000000 + x = 0.904310664 + 0.5333333335 x = 0.904310664 + 0.5333333335 Combine like terms: 0.904310664 + 0.5333333335 = 1.4376439975 x = 1.4376439975 Simplifying x = 1.4376439975Subproblem 2
x + -0.5333333335 = -0.904310664 Simplifying x + -0.5333333335 = -0.904310664 Reorder the terms: -0.5333333335 + x = -0.904310664 Solving -0.5333333335 + x = -0.904310664 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5333333335' to each side of the equation. -0.5333333335 + 0.5333333335 + x = -0.904310664 + 0.5333333335 Combine like terms: -0.5333333335 + 0.5333333335 = 0.0000000000 0.0000000000 + x = -0.904310664 + 0.5333333335 x = -0.904310664 + 0.5333333335 Combine like terms: -0.904310664 + 0.5333333335 = -0.3709773305 x = -0.3709773305 Simplifying x = -0.3709773305Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4376439975, -0.3709773305}
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