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Simplifying x2 + -90x = -180 Reorder the terms: -90x + x2 = -180 Solving -90x + x2 = -180 Solving for variable 'x'. Reorder the terms: 180 + -90x + x2 = -180 + 180 Combine like terms: -180 + 180 = 0 180 + -90x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-180' to each side of the equation. 180 + -90x + -180 + x2 = 0 + -180 Reorder the terms: 180 + -180 + -90x + x2 = 0 + -180 Combine like terms: 180 + -180 = 0 0 + -90x + x2 = 0 + -180 -90x + x2 = 0 + -180 Combine like terms: 0 + -180 = -180 -90x + x2 = -180 The x term is -90x. Take half its coefficient (-45). Square it (2025) and add it to both sides. Add '2025' to each side of the equation. -90x + 2025 + x2 = -180 + 2025 Reorder the terms: 2025 + -90x + x2 = -180 + 2025 Combine like terms: -180 + 2025 = 1845 2025 + -90x + x2 = 1845 Factor a perfect square on the left side: (x + -45)(x + -45) = 1845 Calculate the square root of the right side: 42.95346319 Break this problem into two subproblems by setting (x + -45) equal to 42.95346319 and -42.95346319.Subproblem 1
x + -45 = 42.95346319 Simplifying x + -45 = 42.95346319 Reorder the terms: -45 + x = 42.95346319 Solving -45 + x = 42.95346319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + x = 42.95346319 + 45 Combine like terms: -45 + 45 = 0 0 + x = 42.95346319 + 45 x = 42.95346319 + 45 Combine like terms: 42.95346319 + 45 = 87.95346319 x = 87.95346319 Simplifying x = 87.95346319Subproblem 2
x + -45 = -42.95346319 Simplifying x + -45 = -42.95346319 Reorder the terms: -45 + x = -42.95346319 Solving -45 + x = -42.95346319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + x = -42.95346319 + 45 Combine like terms: -45 + 45 = 0 0 + x = -42.95346319 + 45 x = -42.95346319 + 45 Combine like terms: -42.95346319 + 45 = 2.04653681 x = 2.04653681 Simplifying x = 2.04653681Solution
The solution to the problem is based on the solutions from the subproblems. x = {87.95346319, 2.04653681}
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