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Simplifying 0 = -7 + -92x + x2 Solving 0 = -7 + -92x + x2 Solving for variable 'x'. Combine like terms: 0 + 7 = 7 7 + 92x + -1x2 = -7 + -92x + x2 + 7 + 92x + -1x2 Reorder the terms: 7 + 92x + -1x2 = -7 + 7 + -92x + 92x + x2 + -1x2 Combine like terms: -7 + 7 = 0 7 + 92x + -1x2 = 0 + -92x + 92x + x2 + -1x2 7 + 92x + -1x2 = -92x + 92x + x2 + -1x2 Combine like terms: -92x + 92x = 0 7 + 92x + -1x2 = 0 + x2 + -1x2 7 + 92x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 7 + 92x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -7 + -92x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -92x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -92x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -92x + x2 = 0 + 7 -92x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -92x + x2 = 7 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 = 7 + 2116 Reorder the terms: 2116 + -92x + x2 = 7 + 2116 Combine like terms: 7 + 2116 = 2123 2116 + -92x + x2 = 2123 Factor a perfect square on the left side: (x + -46)(x + -46) = 2123 Calculate the square root of the right side: 46.076024134 Break this problem into two subproblems by setting (x + -46) equal to 46.076024134 and -46.076024134.Subproblem 1
x + -46 = 46.076024134 Simplifying x + -46 = 46.076024134 Reorder the terms: -46 + x = 46.076024134 Solving -46 + x = 46.076024134 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 = 46.076024134 + 46 Combine like terms: -46 + 46 = 0 0 + x = 46.076024134 + 46 x = 46.076024134 + 46 Combine like terms: 46.076024134 + 46 = 92.076024134 x = 92.076024134 Simplifying x = 92.076024134Subproblem 2
x + -46 = -46.076024134 Simplifying x + -46 = -46.076024134 Reorder the terms: -46 + x = -46.076024134 Solving -46 + x = -46.076024134 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 = -46.076024134 + 46 Combine like terms: -46 + 46 = 0 0 + x = -46.076024134 + 46 x = -46.076024134 + 46 Combine like terms: -46.076024134 + 46 = -0.076024134 x = -0.076024134 Simplifying x = -0.076024134Solution
The solution to the problem is based on the solutions from the subproblems. x = {92.076024134, -0.076024134}
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