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Simplifying x2 + 150x + -10 = 0 Reorder the terms: -10 + 150x + x2 = 0 Solving -10 + 150x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 150x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 150x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 150x + x2 = 0 + 10 150x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 150x + x2 = 10 The x term is 150x. Take half its coefficient (75). Square it (5625) and add it to both sides. Add '5625' to each side of the equation. 150x + 5625 + x2 = 10 + 5625 Reorder the terms: 5625 + 150x + x2 = 10 + 5625 Combine like terms: 10 + 5625 = 5635 5625 + 150x + x2 = 5635 Factor a perfect square on the left side: (x + 75)(x + 75) = 5635 Calculate the square root of the right side: 75.066637063 Break this problem into two subproblems by setting (x + 75) equal to 75.066637063 and -75.066637063.Subproblem 1
x + 75 = 75.066637063 Simplifying x + 75 = 75.066637063 Reorder the terms: 75 + x = 75.066637063 Solving 75 + x = 75.066637063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-75' to each side of the equation. 75 + -75 + x = 75.066637063 + -75 Combine like terms: 75 + -75 = 0 0 + x = 75.066637063 + -75 x = 75.066637063 + -75 Combine like terms: 75.066637063 + -75 = 0.066637063 x = 0.066637063 Simplifying x = 0.066637063Subproblem 2
x + 75 = -75.066637063 Simplifying x + 75 = -75.066637063 Reorder the terms: 75 + x = -75.066637063 Solving 75 + x = -75.066637063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-75' to each side of the equation. 75 + -75 + x = -75.066637063 + -75 Combine like terms: 75 + -75 = 0 0 + x = -75.066637063 + -75 x = -75.066637063 + -75 Combine like terms: -75.066637063 + -75 = -150.066637063 x = -150.066637063 Simplifying x = -150.066637063Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.066637063, -150.066637063}
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