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Simplifying x2 + 7x + -2 = 180 Reorder the terms: -2 + 7x + x2 = 180 Solving -2 + 7x + x2 = 180 Solving for variable 'x'. Reorder the terms: -2 + -180 + 7x + x2 = 180 + -180 Combine like terms: -2 + -180 = -182 -182 + 7x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -182 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '182' to each side of the equation. -182 + 7x + 182 + x2 = 0 + 182 Reorder the terms: -182 + 182 + 7x + x2 = 0 + 182 Combine like terms: -182 + 182 = 0 0 + 7x + x2 = 0 + 182 7x + x2 = 0 + 182 Combine like terms: 0 + 182 = 182 7x + x2 = 182 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 = 182 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 182 + 12.25 Combine like terms: 182 + 12.25 = 194.25 12.25 + 7x + x2 = 194.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 194.25 Calculate the square root of the right side: 13.937359865 Break this problem into two subproblems by setting (x + 3.5) equal to 13.937359865 and -13.937359865.Subproblem 1
x + 3.5 = 13.937359865 Simplifying x + 3.5 = 13.937359865 Reorder the terms: 3.5 + x = 13.937359865 Solving 3.5 + x = 13.937359865 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 = 13.937359865 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 13.937359865 + -3.5 x = 13.937359865 + -3.5 Combine like terms: 13.937359865 + -3.5 = 10.437359865 x = 10.437359865 Simplifying x = 10.437359865Subproblem 2
x + 3.5 = -13.937359865 Simplifying x + 3.5 = -13.937359865 Reorder the terms: 3.5 + x = -13.937359865 Solving 3.5 + x = -13.937359865 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 = -13.937359865 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -13.937359865 + -3.5 x = -13.937359865 + -3.5 Combine like terms: -13.937359865 + -3.5 = -17.437359865 x = -17.437359865 Simplifying x = -17.437359865Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.437359865, -17.437359865}
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