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Simplifying x2 + -25x + 32 = 0 Reorder the terms: 32 + -25x + x2 = 0 Solving 32 + -25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-32' to each side of the equation. 32 + -25x + -32 + x2 = 0 + -32 Reorder the terms: 32 + -32 + -25x + x2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -25x + x2 = 0 + -32 -25x + x2 = 0 + -32 Combine like terms: 0 + -32 = -32 -25x + x2 = -32 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 = -32 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -32 + 156.25 Combine like terms: -32 + 156.25 = 124.25 156.25 + -25x + x2 = 124.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 124.25 Calculate the square root of the right side: 11.146748405 Break this problem into two subproblems by setting (x + -12.5) equal to 11.146748405 and -11.146748405.Subproblem 1
x + -12.5 = 11.146748405 Simplifying x + -12.5 = 11.146748405 Reorder the terms: -12.5 + x = 11.146748405 Solving -12.5 + x = 11.146748405 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 = 11.146748405 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 11.146748405 + 12.5 x = 11.146748405 + 12.5 Combine like terms: 11.146748405 + 12.5 = 23.646748405 x = 23.646748405 Simplifying x = 23.646748405Subproblem 2
x + -12.5 = -11.146748405 Simplifying x + -12.5 = -11.146748405 Reorder the terms: -12.5 + x = -11.146748405 Solving -12.5 + x = -11.146748405 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 = -11.146748405 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -11.146748405 + 12.5 x = -11.146748405 + 12.5 Combine like terms: -11.146748405 + 12.5 = 1.353251595 x = 1.353251595 Simplifying x = 1.353251595Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.646748405, 1.353251595}
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