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Simplifying x2 + -1x + -67 * 180 = 0 Multiply -67 * 180 x2 + -1x + -12060 = 0 Reorder the terms: -12060 + -1x + x2 = 0 Solving -12060 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '12060' to each side of the equation. -12060 + -1x + 12060 + x2 = 0 + 12060 Reorder the terms: -12060 + 12060 + -1x + x2 = 0 + 12060 Combine like terms: -12060 + 12060 = 0 0 + -1x + x2 = 0 + 12060 -1x + x2 = 0 + 12060 Combine like terms: 0 + 12060 = 12060 -1x + x2 = 12060 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 12060 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 12060 + 0.25 Combine like terms: 12060 + 0.25 = 12060.25 0.25 + -1x + x2 = 12060.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 12060.25 Calculate the square root of the right side: 109.819169547 Break this problem into two subproblems by setting (x + -0.5) equal to 109.819169547 and -109.819169547.Subproblem 1
x + -0.5 = 109.819169547 Simplifying x + -0.5 = 109.819169547 Reorder the terms: -0.5 + x = 109.819169547 Solving -0.5 + x = 109.819169547 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 109.819169547 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 109.819169547 + 0.5 x = 109.819169547 + 0.5 Combine like terms: 109.819169547 + 0.5 = 110.319169547 x = 110.319169547 Simplifying x = 110.319169547Subproblem 2
x + -0.5 = -109.819169547 Simplifying x + -0.5 = -109.819169547 Reorder the terms: -0.5 + x = -109.819169547 Solving -0.5 + x = -109.819169547 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -109.819169547 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -109.819169547 + 0.5 x = -109.819169547 + 0.5 Combine like terms: -109.819169547 + 0.5 = -109.319169547 x = -109.319169547 Simplifying x = -109.319169547Solution
The solution to the problem is based on the solutions from the subproblems. x = {110.319169547, -109.319169547}
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