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Simplifying x2 + 50x + -175 = 0 Reorder the terms: -175 + 50x + x2 = 0 Solving -175 + 50x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '175' to each side of the equation. -175 + 50x + 175 + x2 = 0 + 175 Reorder the terms: -175 + 175 + 50x + x2 = 0 + 175 Combine like terms: -175 + 175 = 0 0 + 50x + x2 = 0 + 175 50x + x2 = 0 + 175 Combine like terms: 0 + 175 = 175 50x + x2 = 175 The x term is 50x. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50x + 625 + x2 = 175 + 625 Reorder the terms: 625 + 50x + x2 = 175 + 625 Combine like terms: 175 + 625 = 800 625 + 50x + x2 = 800 Factor a perfect square on the left side: (x + 25)(x + 25) = 800 Calculate the square root of the right side: 28.284271247 Break this problem into two subproblems by setting (x + 25) equal to 28.284271247 and -28.284271247.Subproblem 1
x + 25 = 28.284271247 Simplifying x + 25 = 28.284271247 Reorder the terms: 25 + x = 28.284271247 Solving 25 + x = 28.284271247 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = 28.284271247 + -25 Combine like terms: 25 + -25 = 0 0 + x = 28.284271247 + -25 x = 28.284271247 + -25 Combine like terms: 28.284271247 + -25 = 3.284271247 x = 3.284271247 Simplifying x = 3.284271247Subproblem 2
x + 25 = -28.284271247 Simplifying x + 25 = -28.284271247 Reorder the terms: 25 + x = -28.284271247 Solving 25 + x = -28.284271247 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = -28.284271247 + -25 Combine like terms: 25 + -25 = 0 0 + x = -28.284271247 + -25 x = -28.284271247 + -25 Combine like terms: -28.284271247 + -25 = -53.284271247 x = -53.284271247 Simplifying x = -53.284271247Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.284271247, -53.284271247}
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