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Simplifying 0.5x2 = 8x + -0.625 Reorder the terms: 0.5x2 = -0.625 + 8x Solving 0.5x2 = -0.625 + 8x Solving for variable 'x'. Reorder the terms: 0.625 + -8x + 0.5x2 = -0.625 + 8x + 0.625 + -8x Reorder the terms: 0.625 + -8x + 0.5x2 = -0.625 + 0.625 + 8x + -8x Combine like terms: -0.625 + 0.625 = 0.000 0.625 + -8x + 0.5x2 = 0.000 + 8x + -8x 0.625 + -8x + 0.5x2 = 8x + -8x Combine like terms: 8x + -8x = 0 0.625 + -8x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 1.25 + -16x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -16x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -16x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -16x + x2 = 0 + -1.25 -16x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -16x + x2 = -1.25 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = -1.25 + 64 Reorder the terms: 64 + -16x + x2 = -1.25 + 64 Combine like terms: -1.25 + 64 = 62.75 64 + -16x + x2 = 62.75 Factor a perfect square on the left side: (x + -8)(x + -8) = 62.75 Calculate the square root of the right side: 7.921489759 Break this problem into two subproblems by setting (x + -8) equal to 7.921489759 and -7.921489759.Subproblem 1
x + -8 = 7.921489759 Simplifying x + -8 = 7.921489759 Reorder the terms: -8 + x = 7.921489759 Solving -8 + x = 7.921489759 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 7.921489759 + 8 Combine like terms: -8 + 8 = 0 0 + x = 7.921489759 + 8 x = 7.921489759 + 8 Combine like terms: 7.921489759 + 8 = 15.921489759 x = 15.921489759 Simplifying x = 15.921489759Subproblem 2
x + -8 = -7.921489759 Simplifying x + -8 = -7.921489759 Reorder the terms: -8 + x = -7.921489759 Solving -8 + x = -7.921489759 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -7.921489759 + 8 Combine like terms: -8 + 8 = 0 0 + x = -7.921489759 + 8 x = -7.921489759 + 8 Combine like terms: -7.921489759 + 8 = 0.078510241 x = 0.078510241 Simplifying x = 0.078510241Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.921489759, 0.078510241}
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