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Simplifying (2x2) + -48x + -1157 = 0 Reorder the terms: -1157 + -48x + (2x2) = 0 Solving -1157 + -48x + (2x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -578.5 + -24x + x2 = 0 Move the constant term to the right: Add '578.5' to each side of the equation. -578.5 + -24x + 578.5 + x2 = 0 + 578.5 Reorder the terms: -578.5 + 578.5 + -24x + x2 = 0 + 578.5 Combine like terms: -578.5 + 578.5 = 0.0 0.0 + -24x + x2 = 0 + 578.5 -24x + x2 = 0 + 578.5 Combine like terms: 0 + 578.5 = 578.5 -24x + x2 = 578.5 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = 578.5 + 144 Reorder the terms: 144 + -24x + x2 = 578.5 + 144 Combine like terms: 578.5 + 144 = 722.5 144 + -24x + x2 = 722.5 Factor a perfect square on the left side: ((x) + -12)((x) + -12) = 722.5 Calculate the square root of the right side: 26.879360111 Break this problem into two subproblems by setting ((x) + -12) equal to 26.879360111 and -26.879360111.Subproblem 1
(x) + -12 = 26.879360111 Simplifying (x) + -12 = 26.879360111 x + -12 = 26.879360111 Reorder the terms: -12 + x = 26.879360111 Solving -12 + x = 26.879360111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 26.879360111 + 12 Combine like terms: -12 + 12 = 0 0 + x = 26.879360111 + 12 x = 26.879360111 + 12 Combine like terms: 26.879360111 + 12 = 38.879360111 x = 38.879360111 Simplifying x = 38.879360111Subproblem 2
(x) + -12 = -26.879360111 Simplifying (x) + -12 = -26.879360111 x + -12 = -26.879360111 Reorder the terms: -12 + x = -26.879360111 Solving -12 + x = -26.879360111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -26.879360111 + 12 Combine like terms: -12 + 12 = 0 0 + x = -26.879360111 + 12 x = -26.879360111 + 12 Combine like terms: -26.879360111 + 12 = -14.879360111 x = -14.879360111 Simplifying x = -14.879360111Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.879360111, -14.879360111}
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