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Simplifying x2 + 8x + 8 = 180 Reorder the terms: 8 + 8x + x2 = 180 Solving 8 + 8x + x2 = 180 Solving for variable 'x'. Reorder the terms: 8 + -180 + 8x + x2 = 180 + -180 Combine like terms: 8 + -180 = -172 -172 + 8x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -172 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '172' to each side of the equation. -172 + 8x + 172 + x2 = 0 + 172 Reorder the terms: -172 + 172 + 8x + x2 = 0 + 172 Combine like terms: -172 + 172 = 0 0 + 8x + x2 = 0 + 172 8x + x2 = 0 + 172 Combine like terms: 0 + 172 = 172 8x + x2 = 172 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 172 + 16 Reorder the terms: 16 + 8x + x2 = 172 + 16 Combine like terms: 172 + 16 = 188 16 + 8x + x2 = 188 Factor a perfect square on the left side: (x + 4)(x + 4) = 188 Calculate the square root of the right side: 13.711309201 Break this problem into two subproblems by setting (x + 4) equal to 13.711309201 and -13.711309201.Subproblem 1
x + 4 = 13.711309201 Simplifying x + 4 = 13.711309201 Reorder the terms: 4 + x = 13.711309201 Solving 4 + x = 13.711309201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 13.711309201 + -4 Combine like terms: 4 + -4 = 0 0 + x = 13.711309201 + -4 x = 13.711309201 + -4 Combine like terms: 13.711309201 + -4 = 9.711309201 x = 9.711309201 Simplifying x = 9.711309201Subproblem 2
x + 4 = -13.711309201 Simplifying x + 4 = -13.711309201 Reorder the terms: 4 + x = -13.711309201 Solving 4 + x = -13.711309201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -13.711309201 + -4 Combine like terms: 4 + -4 = 0 0 + x = -13.711309201 + -4 x = -13.711309201 + -4 Combine like terms: -13.711309201 + -4 = -17.711309201 x = -17.711309201 Simplifying x = -17.711309201Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.711309201, -17.711309201}
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