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Simplifying x2 + -75x + 100 = 0 Reorder the terms: 100 + -75x + x2 = 0 Solving 100 + -75x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-100' to each side of the equation. 100 + -75x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + -75x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -75x + x2 = 0 + -100 -75x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 -75x + x2 = -100 The x term is -75x. Take half its coefficient (-37.5). Square it (1406.25) and add it to both sides. Add '1406.25' to each side of the equation. -75x + 1406.25 + x2 = -100 + 1406.25 Reorder the terms: 1406.25 + -75x + x2 = -100 + 1406.25 Combine like terms: -100 + 1406.25 = 1306.25 1406.25 + -75x + x2 = 1306.25 Factor a perfect square on the left side: (x + -37.5)(x + -37.5) = 1306.25 Calculate the square root of the right side: 36.142080737 Break this problem into two subproblems by setting (x + -37.5) equal to 36.142080737 and -36.142080737.Subproblem 1
x + -37.5 = 36.142080737 Simplifying x + -37.5 = 36.142080737 Reorder the terms: -37.5 + x = 36.142080737 Solving -37.5 + x = 36.142080737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '37.5' to each side of the equation. -37.5 + 37.5 + x = 36.142080737 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + x = 36.142080737 + 37.5 x = 36.142080737 + 37.5 Combine like terms: 36.142080737 + 37.5 = 73.642080737 x = 73.642080737 Simplifying x = 73.642080737Subproblem 2
x + -37.5 = -36.142080737 Simplifying x + -37.5 = -36.142080737 Reorder the terms: -37.5 + x = -36.142080737 Solving -37.5 + x = -36.142080737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '37.5' to each side of the equation. -37.5 + 37.5 + x = -36.142080737 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + x = -36.142080737 + 37.5 x = -36.142080737 + 37.5 Combine like terms: -36.142080737 + 37.5 = 1.357919263 x = 1.357919263 Simplifying x = 1.357919263Solution
The solution to the problem is based on the solutions from the subproblems. x = {73.642080737, 1.357919263}
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