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Simplifying x2 + -53x = 222 Reorder the terms: -53x + x2 = 222 Solving -53x + x2 = 222 Solving for variable 'x'. Reorder the terms: -222 + -53x + x2 = 222 + -222 Combine like terms: 222 + -222 = 0 -222 + -53x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '222' to each side of the equation. -222 + -53x + 222 + x2 = 0 + 222 Reorder the terms: -222 + 222 + -53x + x2 = 0 + 222 Combine like terms: -222 + 222 = 0 0 + -53x + x2 = 0 + 222 -53x + x2 = 0 + 222 Combine like terms: 0 + 222 = 222 -53x + x2 = 222 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 = 222 + 702.25 Reorder the terms: 702.25 + -53x + x2 = 222 + 702.25 Combine like terms: 222 + 702.25 = 924.25 702.25 + -53x + x2 = 924.25 Factor a perfect square on the left side: (x + -26.5)(x + -26.5) = 924.25 Calculate the square root of the right side: 30.401480227 Break this problem into two subproblems by setting (x + -26.5) equal to 30.401480227 and -30.401480227.Subproblem 1
x + -26.5 = 30.401480227 Simplifying x + -26.5 = 30.401480227 Reorder the terms: -26.5 + x = 30.401480227 Solving -26.5 + x = 30.401480227 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 = 30.401480227 + 26.5 Combine like terms: -26.5 + 26.5 = 0.0 0.0 + x = 30.401480227 + 26.5 x = 30.401480227 + 26.5 Combine like terms: 30.401480227 + 26.5 = 56.901480227 x = 56.901480227 Simplifying x = 56.901480227Subproblem 2
x + -26.5 = -30.401480227 Simplifying x + -26.5 = -30.401480227 Reorder the terms: -26.5 + x = -30.401480227 Solving -26.5 + x = -30.401480227 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 = -30.401480227 + 26.5 Combine like terms: -26.5 + 26.5 = 0.0 0.0 + x = -30.401480227 + 26.5 x = -30.401480227 + 26.5 Combine like terms: -30.401480227 + 26.5 = -3.901480227 x = -3.901480227 Simplifying x = -3.901480227Solution
The solution to the problem is based on the solutions from the subproblems. x = {56.901480227, -3.901480227}
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