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Simplifying x2 + -7x + -180 = 0 Reorder the terms: -180 + -7x + x2 = 0 Solving -180 + -7x + 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 + -7x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + -7x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + -7x + x2 = 0 + 180 -7x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 -7x + x2 = 180 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 180 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 180 + 12.25 Combine like terms: 180 + 12.25 = 192.25 12.25 + -7x + x2 = 192.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 192.25 Calculate the square root of the right side: 13.865424624 Break this problem into two subproblems by setting (x + -3.5) equal to 13.865424624 and -13.865424624.Subproblem 1
x + -3.5 = 13.865424624 Simplifying x + -3.5 = 13.865424624 Reorder the terms: -3.5 + x = 13.865424624 Solving -3.5 + x = 13.865424624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 13.865424624 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 13.865424624 + 3.5 x = 13.865424624 + 3.5 Combine like terms: 13.865424624 + 3.5 = 17.365424624 x = 17.365424624 Simplifying x = 17.365424624Subproblem 2
x + -3.5 = -13.865424624 Simplifying x + -3.5 = -13.865424624 Reorder the terms: -3.5 + x = -13.865424624 Solving -3.5 + x = -13.865424624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -13.865424624 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -13.865424624 + 3.5 x = -13.865424624 + 3.5 Combine like terms: -13.865424624 + 3.5 = -10.365424624 x = -10.365424624 Simplifying x = -10.365424624Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.365424624, -10.365424624}
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