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Simplifying -1x2 + 8x + 37 = 0 Reorder the terms: 37 + 8x + -1x2 = 0 Solving 37 + 8x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -37 + -8x + x2 = 0 Move the constant term to the right: Add '37' to each side of the equation. -37 + -8x + 37 + x2 = 0 + 37 Reorder the terms: -37 + 37 + -8x + x2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + -8x + x2 = 0 + 37 -8x + x2 = 0 + 37 Combine like terms: 0 + 37 = 37 -8x + x2 = 37 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 37 + 16 Reorder the terms: 16 + -8x + x2 = 37 + 16 Combine like terms: 37 + 16 = 53 16 + -8x + x2 = 53 Factor a perfect square on the left side: (x + -4)(x + -4) = 53 Calculate the square root of the right side: 7.280109889 Break this problem into two subproblems by setting (x + -4) equal to 7.280109889 and -7.280109889.Subproblem 1
x + -4 = 7.280109889 Simplifying x + -4 = 7.280109889 Reorder the terms: -4 + x = 7.280109889 Solving -4 + x = 7.280109889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 7.280109889 + 4 Combine like terms: -4 + 4 = 0 0 + x = 7.280109889 + 4 x = 7.280109889 + 4 Combine like terms: 7.280109889 + 4 = 11.280109889 x = 11.280109889 Simplifying x = 11.280109889Subproblem 2
x + -4 = -7.280109889 Simplifying x + -4 = -7.280109889 Reorder the terms: -4 + x = -7.280109889 Solving -4 + x = -7.280109889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -7.280109889 + 4 Combine like terms: -4 + 4 = 0 0 + x = -7.280109889 + 4 x = -7.280109889 + 4 Combine like terms: -7.280109889 + 4 = -3.280109889 x = -3.280109889 Simplifying x = -3.280109889Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.280109889, -3.280109889}
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