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Simplifying x2 + -53x + 200 = 0 Reorder the terms: 200 + -53x + x2 = 0 Solving 200 + -53x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-200' to each side of the equation. 200 + -53x + -200 + x2 = 0 + -200 Reorder the terms: 200 + -200 + -53x + x2 = 0 + -200 Combine like terms: 200 + -200 = 0 0 + -53x + x2 = 0 + -200 -53x + x2 = 0 + -200 Combine like terms: 0 + -200 = -200 -53x + x2 = -200 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 = -200 + 702.25 Reorder the terms: 702.25 + -53x + x2 = -200 + 702.25 Combine like terms: -200 + 702.25 = 502.25 702.25 + -53x + x2 = 502.25 Factor a perfect square on the left side: (x + -26.5)(x + -26.5) = 502.25 Calculate the square root of the right side: 22.410934831 Break this problem into two subproblems by setting (x + -26.5) equal to 22.410934831 and -22.410934831.Subproblem 1
x + -26.5 = 22.410934831 Simplifying x + -26.5 = 22.410934831 Reorder the terms: -26.5 + x = 22.410934831 Solving -26.5 + x = 22.410934831 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 = 22.410934831 + 26.5 Combine like terms: -26.5 + 26.5 = 0.0 0.0 + x = 22.410934831 + 26.5 x = 22.410934831 + 26.5 Combine like terms: 22.410934831 + 26.5 = 48.910934831 x = 48.910934831 Simplifying x = 48.910934831Subproblem 2
x + -26.5 = -22.410934831 Simplifying x + -26.5 = -22.410934831 Reorder the terms: -26.5 + x = -22.410934831 Solving -26.5 + x = -22.410934831 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 = -22.410934831 + 26.5 Combine like terms: -26.5 + 26.5 = 0.0 0.0 + x = -22.410934831 + 26.5 x = -22.410934831 + 26.5 Combine like terms: -22.410934831 + 26.5 = 4.089065169 x = 4.089065169 Simplifying x = 4.089065169Solution
The solution to the problem is based on the solutions from the subproblems. x = {48.910934831, 4.089065169}
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