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Simplifying x2 + -42x + 180 = 0 Reorder the terms: 180 + -42x + x2 = 0 Solving 180 + -42x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-180' to each side of the equation. 180 + -42x + -180 + x2 = 0 + -180 Reorder the terms: 180 + -180 + -42x + x2 = 0 + -180 Combine like terms: 180 + -180 = 0 0 + -42x + x2 = 0 + -180 -42x + x2 = 0 + -180 Combine like terms: 0 + -180 = -180 -42x + x2 = -180 The x term is -42x. Take half its coefficient (-21). Square it (441) and add it to both sides. Add '441' to each side of the equation. -42x + 441 + x2 = -180 + 441 Reorder the terms: 441 + -42x + x2 = -180 + 441 Combine like terms: -180 + 441 = 261 441 + -42x + x2 = 261 Factor a perfect square on the left side: (x + -21)(x + -21) = 261 Calculate the square root of the right side: 16.155494421 Break this problem into two subproblems by setting (x + -21) equal to 16.155494421 and -16.155494421.Subproblem 1
x + -21 = 16.155494421 Simplifying x + -21 = 16.155494421 Reorder the terms: -21 + x = 16.155494421 Solving -21 + x = 16.155494421 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + x = 16.155494421 + 21 Combine like terms: -21 + 21 = 0 0 + x = 16.155494421 + 21 x = 16.155494421 + 21 Combine like terms: 16.155494421 + 21 = 37.155494421 x = 37.155494421 Simplifying x = 37.155494421Subproblem 2
x + -21 = -16.155494421 Simplifying x + -21 = -16.155494421 Reorder the terms: -21 + x = -16.155494421 Solving -21 + x = -16.155494421 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + x = -16.155494421 + 21 Combine like terms: -21 + 21 = 0 0 + x = -16.155494421 + 21 x = -16.155494421 + 21 Combine like terms: -16.155494421 + 21 = 4.844505579 x = 4.844505579 Simplifying x = 4.844505579Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.155494421, 4.844505579}
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