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Simplifying x2 + -53x + -500 = 0 Reorder the terms: -500 + -53x + x2 = 0 Solving -500 + -53x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '500' to each side of the equation. -500 + -53x + 500 + x2 = 0 + 500 Reorder the terms: -500 + 500 + -53x + x2 = 0 + 500 Combine like terms: -500 + 500 = 0 0 + -53x + x2 = 0 + 500 -53x + x2 = 0 + 500 Combine like terms: 0 + 500 = 500 -53x + x2 = 500 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 = 500 + 702.25 Reorder the terms: 702.25 + -53x + x2 = 500 + 702.25 Combine like terms: 500 + 702.25 = 1202.25 702.25 + -53x + x2 = 1202.25 Factor a perfect square on the left side: (x + -26.5)(x + -26.5) = 1202.25 Calculate the square root of the right side: 34.673476895 Break this problem into two subproblems by setting (x + -26.5) equal to 34.673476895 and -34.673476895.Subproblem 1
x + -26.5 = 34.673476895 Simplifying x + -26.5 = 34.673476895 Reorder the terms: -26.5 + x = 34.673476895 Solving -26.5 + x = 34.673476895 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 = 34.673476895 + 26.5 Combine like terms: -26.5 + 26.5 = 0.0 0.0 + x = 34.673476895 + 26.5 x = 34.673476895 + 26.5 Combine like terms: 34.673476895 + 26.5 = 61.173476895 x = 61.173476895 Simplifying x = 61.173476895Subproblem 2
x + -26.5 = -34.673476895 Simplifying x + -26.5 = -34.673476895 Reorder the terms: -26.5 + x = -34.673476895 Solving -26.5 + x = -34.673476895 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 = -34.673476895 + 26.5 Combine like terms: -26.5 + 26.5 = 0.0 0.0 + x = -34.673476895 + 26.5 x = -34.673476895 + 26.5 Combine like terms: -34.673476895 + 26.5 = -8.173476895 x = -8.173476895 Simplifying x = -8.173476895Solution
The solution to the problem is based on the solutions from the subproblems. x = {61.173476895, -8.173476895}
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