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Simplifying x2 + -16x + -9 = 180 Reorder the terms: -9 + -16x + x2 = 180 Solving -9 + -16x + x2 = 180 Solving for variable 'x'. Reorder the terms: -9 + -180 + -16x + x2 = 180 + -180 Combine like terms: -9 + -180 = -189 -189 + -16x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -189 + -16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '189' to each side of the equation. -189 + -16x + 189 + x2 = 0 + 189 Reorder the terms: -189 + 189 + -16x + x2 = 0 + 189 Combine like terms: -189 + 189 = 0 0 + -16x + x2 = 0 + 189 -16x + x2 = 0 + 189 Combine like terms: 0 + 189 = 189 -16x + x2 = 189 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = 189 + 64 Reorder the terms: 64 + -16x + x2 = 189 + 64 Combine like terms: 189 + 64 = 253 64 + -16x + x2 = 253 Factor a perfect square on the left side: (x + -8)(x + -8) = 253 Calculate the square root of the right side: 15.905973721 Break this problem into two subproblems by setting (x + -8) equal to 15.905973721 and -15.905973721.Subproblem 1
x + -8 = 15.905973721 Simplifying x + -8 = 15.905973721 Reorder the terms: -8 + x = 15.905973721 Solving -8 + x = 15.905973721 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 15.905973721 + 8 Combine like terms: -8 + 8 = 0 0 + x = 15.905973721 + 8 x = 15.905973721 + 8 Combine like terms: 15.905973721 + 8 = 23.905973721 x = 23.905973721 Simplifying x = 23.905973721Subproblem 2
x + -8 = -15.905973721 Simplifying x + -8 = -15.905973721 Reorder the terms: -8 + x = -15.905973721 Solving -8 + x = -15.905973721 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -15.905973721 + 8 Combine like terms: -8 + 8 = 0 0 + x = -15.905973721 + 8 x = -15.905973721 + 8 Combine like terms: -15.905973721 + 8 = -7.905973721 x = -7.905973721 Simplifying x = -7.905973721Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.905973721, -7.905973721}
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