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Simplifying 53x + -1x2 = 144 Solving 53x + -1x2 = 144 Solving for variable 'x'. Reorder the terms: -144 + 53x + -1x2 = 144 + -144 Combine like terms: 144 + -144 = 0 -144 + 53x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 144 + -53x + x2 = 0 Move the constant term to the right: Add '-144' to each side of the equation. 144 + -53x + -144 + x2 = 0 + -144 Reorder the terms: 144 + -144 + -53x + x2 = 0 + -144 Combine like terms: 144 + -144 = 0 0 + -53x + x2 = 0 + -144 -53x + x2 = 0 + -144 Combine like terms: 0 + -144 = -144 -53x + x2 = -144 The x term is -53x. Take half its coefficient (-26.5). Square it (702.25) and add it to both sides. Add '702.25' to each side of the equation. -53x + 702.25 + x2 = -144 + 702.25 Reorder the terms: 702.25 + -53x + x2 = -144 + 702.25 Combine like terms: -144 + 702.25 = 558.25 702.25 + -53x + x2 = 558.25 Factor a perfect square on the left side: (x + -26.5)(x + -26.5) = 558.25 Calculate the square root of the right side: 23.627314701 Break this problem into two subproblems by setting (x + -26.5) equal to 23.627314701 and -23.627314701.Subproblem 1
x + -26.5 = 23.627314701 Simplifying x + -26.5 = 23.627314701 Reorder the terms: -26.5 + x = 23.627314701 Solving -26.5 + x = 23.627314701 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26.5' to each side of the equation. -26.5 + 26.5 + x = 23.627314701 + 26.5 Combine like terms: -26.5 + 26.5 = 0.0 0.0 + x = 23.627314701 + 26.5 x = 23.627314701 + 26.5 Combine like terms: 23.627314701 + 26.5 = 50.127314701 x = 50.127314701 Simplifying x = 50.127314701Subproblem 2
x + -26.5 = -23.627314701 Simplifying x + -26.5 = -23.627314701 Reorder the terms: -26.5 + x = -23.627314701 Solving -26.5 + x = -23.627314701 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26.5' to each side of the equation. -26.5 + 26.5 + x = -23.627314701 + 26.5 Combine like terms: -26.5 + 26.5 = 0.0 0.0 + x = -23.627314701 + 26.5 x = -23.627314701 + 26.5 Combine like terms: -23.627314701 + 26.5 = 2.872685299 x = 2.872685299 Simplifying x = 2.872685299Solution
The solution to the problem is based on the solutions from the subproblems. x = {50.127314701, 2.872685299}
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