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Simplifying -0.5x2 + -46x + -10 = 0 Reorder the terms: -10 + -46x + -0.5x2 = 0 Solving -10 + -46x + -0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. 20 + 92x + x2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + 92x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + 92x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 92x + x2 = 0 + -20 92x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 92x + x2 = -20 The x term is 92x. Take half its coefficient (46). Square it (2116) and add it to both sides. Add '2116' to each side of the equation. 92x + 2116 + x2 = -20 + 2116 Reorder the terms: 2116 + 92x + x2 = -20 + 2116 Combine like terms: -20 + 2116 = 2096 2116 + 92x + x2 = 2096 Factor a perfect square on the left side: (x + 46)(x + 46) = 2096 Calculate the square root of the right side: 45.782092569 Break this problem into two subproblems by setting (x + 46) equal to 45.782092569 and -45.782092569.Subproblem 1
x + 46 = 45.782092569 Simplifying x + 46 = 45.782092569 Reorder the terms: 46 + x = 45.782092569 Solving 46 + x = 45.782092569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-46' to each side of the equation. 46 + -46 + x = 45.782092569 + -46 Combine like terms: 46 + -46 = 0 0 + x = 45.782092569 + -46 x = 45.782092569 + -46 Combine like terms: 45.782092569 + -46 = -0.217907431 x = -0.217907431 Simplifying x = -0.217907431Subproblem 2
x + 46 = -45.782092569 Simplifying x + 46 = -45.782092569 Reorder the terms: 46 + x = -45.782092569 Solving 46 + x = -45.782092569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-46' to each side of the equation. 46 + -46 + x = -45.782092569 + -46 Combine like terms: 46 + -46 = 0 0 + x = -45.782092569 + -46 x = -45.782092569 + -46 Combine like terms: -45.782092569 + -46 = -91.782092569 x = -91.782092569 Simplifying x = -91.782092569Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.217907431, -91.782092569}
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