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Simplifying x2 + -25x + 13 = 0 Reorder the terms: 13 + -25x + x2 = 0 Solving 13 + -25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + -25x + -13 + x2 = 0 + -13 Reorder the terms: 13 + -13 + -25x + x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -25x + x2 = 0 + -13 -25x + x2 = 0 + -13 Combine like terms: 0 + -13 = -13 -25x + x2 = -13 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 = -13 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -13 + 156.25 Combine like terms: -13 + 156.25 = 143.25 156.25 + -25x + x2 = 143.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 143.25 Calculate the square root of the right side: 11.968709204 Break this problem into two subproblems by setting (x + -12.5) equal to 11.968709204 and -11.968709204.Subproblem 1
x + -12.5 = 11.968709204 Simplifying x + -12.5 = 11.968709204 Reorder the terms: -12.5 + x = 11.968709204 Solving -12.5 + x = 11.968709204 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 = 11.968709204 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 11.968709204 + 12.5 x = 11.968709204 + 12.5 Combine like terms: 11.968709204 + 12.5 = 24.468709204 x = 24.468709204 Simplifying x = 24.468709204Subproblem 2
x + -12.5 = -11.968709204 Simplifying x + -12.5 = -11.968709204 Reorder the terms: -12.5 + x = -11.968709204 Solving -12.5 + x = -11.968709204 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 = -11.968709204 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -11.968709204 + 12.5 x = -11.968709204 + 12.5 Combine like terms: -11.968709204 + 12.5 = 0.531290796 x = 0.531290796 Simplifying x = 0.531290796Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.468709204, 0.531290796}
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