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Simplifying x2 + -96x + -180 = 0 Reorder the terms: -180 + -96x + x2 = 0 Solving -180 + -96x + 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 + -96x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + -96x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + -96x + x2 = 0 + 180 -96x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 -96x + x2 = 180 The x term is -96x. Take half its coefficient (-48). Square it (2304) and add it to both sides. Add '2304' to each side of the equation. -96x + 2304 + x2 = 180 + 2304 Reorder the terms: 2304 + -96x + x2 = 180 + 2304 Combine like terms: 180 + 2304 = 2484 2304 + -96x + x2 = 2484 Factor a perfect square on the left side: (x + -48)(x + -48) = 2484 Calculate the square root of the right side: 49.839743178 Break this problem into two subproblems by setting (x + -48) equal to 49.839743178 and -49.839743178.Subproblem 1
x + -48 = 49.839743178 Simplifying x + -48 = 49.839743178 Reorder the terms: -48 + x = 49.839743178 Solving -48 + x = 49.839743178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '48' to each side of the equation. -48 + 48 + x = 49.839743178 + 48 Combine like terms: -48 + 48 = 0 0 + x = 49.839743178 + 48 x = 49.839743178 + 48 Combine like terms: 49.839743178 + 48 = 97.839743178 x = 97.839743178 Simplifying x = 97.839743178Subproblem 2
x + -48 = -49.839743178 Simplifying x + -48 = -49.839743178 Reorder the terms: -48 + x = -49.839743178 Solving -48 + x = -49.839743178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '48' to each side of the equation. -48 + 48 + x = -49.839743178 + 48 Combine like terms: -48 + 48 = 0 0 + x = -49.839743178 + 48 x = -49.839743178 + 48 Combine like terms: -49.839743178 + 48 = -1.839743178 x = -1.839743178 Simplifying x = -1.839743178Solution
The solution to the problem is based on the solutions from the subproblems. x = {97.839743178, -1.839743178}
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