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Simplifying x2 + 48x + -180 = 0 Reorder the terms: -180 + 48x + x2 = 0 Solving -180 + 48x + 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 + 48x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + 48x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 48x + x2 = 0 + 180 48x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 48x + x2 = 180 The x term is 48x. Take half its coefficient (24). Square it (576) and add it to both sides. Add '576' to each side of the equation. 48x + 576 + x2 = 180 + 576 Reorder the terms: 576 + 48x + x2 = 180 + 576 Combine like terms: 180 + 576 = 756 576 + 48x + x2 = 756 Factor a perfect square on the left side: (x + 24)(x + 24) = 756 Calculate the square root of the right side: 27.49545417 Break this problem into two subproblems by setting (x + 24) equal to 27.49545417 and -27.49545417.Subproblem 1
x + 24 = 27.49545417 Simplifying x + 24 = 27.49545417 Reorder the terms: 24 + x = 27.49545417 Solving 24 + x = 27.49545417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + x = 27.49545417 + -24 Combine like terms: 24 + -24 = 0 0 + x = 27.49545417 + -24 x = 27.49545417 + -24 Combine like terms: 27.49545417 + -24 = 3.49545417 x = 3.49545417 Simplifying x = 3.49545417Subproblem 2
x + 24 = -27.49545417 Simplifying x + 24 = -27.49545417 Reorder the terms: 24 + x = -27.49545417 Solving 24 + x = -27.49545417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + x = -27.49545417 + -24 Combine like terms: 24 + -24 = 0 0 + x = -27.49545417 + -24 x = -27.49545417 + -24 Combine like terms: -27.49545417 + -24 = -51.49545417 x = -51.49545417 Simplifying x = -51.49545417Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.49545417, -51.49545417}
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