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Simplifying x2 + -8x = 25 Reorder the terms: -8x + x2 = 25 Solving -8x + x2 = 25 Solving for variable 'x'. Reorder the terms: -25 + -8x + x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + -8x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + -8x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -8x + x2 = 0 + 25 -8x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 -8x + x2 = 25 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 25 + 16 Reorder the terms: 16 + -8x + x2 = 25 + 16 Combine like terms: 25 + 16 = 41 16 + -8x + x2 = 41 Factor a perfect square on the left side: (x + -4)(x + -4) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (x + -4) equal to 6.403124237 and -6.403124237.Subproblem 1
x + -4 = 6.403124237 Simplifying x + -4 = 6.403124237 Reorder the terms: -4 + x = 6.403124237 Solving -4 + x = 6.403124237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 6.403124237 + 4 Combine like terms: -4 + 4 = 0 0 + x = 6.403124237 + 4 x = 6.403124237 + 4 Combine like terms: 6.403124237 + 4 = 10.403124237 x = 10.403124237 Simplifying x = 10.403124237Subproblem 2
x + -4 = -6.403124237 Simplifying x + -4 = -6.403124237 Reorder the terms: -4 + x = -6.403124237 Solving -4 + x = -6.403124237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -6.403124237 + 4 Combine like terms: -4 + 4 = 0 0 + x = -6.403124237 + 4 x = -6.403124237 + 4 Combine like terms: -6.403124237 + 4 = -2.403124237 x = -2.403124237 Simplifying x = -2.403124237Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.403124237, -2.403124237}
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