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Simplifying 0.5x2 + 8x = -7 Reorder the terms: 8x + 0.5x2 = -7 Solving 8x + 0.5x2 = -7 Solving for variable 'x'. Reorder the terms: 7 + 8x + 0.5x2 = -7 + 7 Combine like terms: -7 + 7 = 0 7 + 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'. 14 + 16x + x2 = 0 Move the constant term to the right: Add '-14' to each side of the equation. 14 + 16x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + 16x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 16x + x2 = 0 + -14 16x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 16x + x2 = -14 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 = -14 + 64 Reorder the terms: 64 + 16x + x2 = -14 + 64 Combine like terms: -14 + 64 = 50 64 + 16x + x2 = 50 Factor a perfect square on the left side: (x + 8)(x + 8) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (x + 8) equal to 7.071067812 and -7.071067812.Subproblem 1
x + 8 = 7.071067812 Simplifying x + 8 = 7.071067812 Reorder the terms: 8 + x = 7.071067812 Solving 8 + x = 7.071067812 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 = 7.071067812 + -8 Combine like terms: 8 + -8 = 0 0 + x = 7.071067812 + -8 x = 7.071067812 + -8 Combine like terms: 7.071067812 + -8 = -0.928932188 x = -0.928932188 Simplifying x = -0.928932188Subproblem 2
x + 8 = -7.071067812 Simplifying x + 8 = -7.071067812 Reorder the terms: 8 + x = -7.071067812 Solving 8 + x = -7.071067812 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 = -7.071067812 + -8 Combine like terms: 8 + -8 = 0 0 + x = -7.071067812 + -8 x = -7.071067812 + -8 Combine like terms: -7.071067812 + -8 = -15.071067812 x = -15.071067812 Simplifying x = -15.071067812Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.928932188, -15.071067812}
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