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Simplifying x2 + -25x + 3 = 0 Reorder the terms: 3 + -25x + x2 = 0 Solving 3 + -25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -25x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -25x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -25x + x2 = 0 + -3 -25x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -25x + x2 = -3 The x term is -25x. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25x + 156.25 + x2 = -3 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -3 + 156.25 Combine like terms: -3 + 156.25 = 153.25 156.25 + -25x + x2 = 153.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 153.25 Calculate the square root of the right side: 12.379418403 Break this problem into two subproblems by setting (x + -12.5) equal to 12.379418403 and -12.379418403.Subproblem 1
x + -12.5 = 12.379418403 Simplifying x + -12.5 = 12.379418403 Reorder the terms: -12.5 + x = 12.379418403 Solving -12.5 + x = 12.379418403 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = 12.379418403 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 12.379418403 + 12.5 x = 12.379418403 + 12.5 Combine like terms: 12.379418403 + 12.5 = 24.879418403 x = 24.879418403 Simplifying x = 24.879418403Subproblem 2
x + -12.5 = -12.379418403 Simplifying x + -12.5 = -12.379418403 Reorder the terms: -12.5 + x = -12.379418403 Solving -12.5 + x = -12.379418403 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = -12.379418403 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -12.379418403 + 12.5 x = -12.379418403 + 12.5 Combine like terms: -12.379418403 + 12.5 = 0.120581597 x = 0.120581597 Simplifying x = 0.120581597Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.879418403, 0.120581597}
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