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Simplifying x2 + 18x + 81 + -4 = 187 Reorder the terms: 81 + -4 + 18x + x2 = 187 Combine like terms: 81 + -4 = 77 77 + 18x + x2 = 187 Solving 77 + 18x + x2 = 187 Solving for variable 'x'. Reorder the terms: 77 + -187 + 18x + x2 = 187 + -187 Combine like terms: 77 + -187 = -110 -110 + 18x + x2 = 187 + -187 Combine like terms: 187 + -187 = 0 -110 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '110' to each side of the equation. -110 + 18x + 110 + x2 = 0 + 110 Reorder the terms: -110 + 110 + 18x + x2 = 0 + 110 Combine like terms: -110 + 110 = 0 0 + 18x + x2 = 0 + 110 18x + x2 = 0 + 110 Combine like terms: 0 + 110 = 110 18x + x2 = 110 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = 110 + 81 Reorder the terms: 81 + 18x + x2 = 110 + 81 Combine like terms: 110 + 81 = 191 81 + 18x + x2 = 191 Factor a perfect square on the left side: (x + 9)(x + 9) = 191 Calculate the square root of the right side: 13.820274961 Break this problem into two subproblems by setting (x + 9) equal to 13.820274961 and -13.820274961.Subproblem 1
x + 9 = 13.820274961 Simplifying x + 9 = 13.820274961 Reorder the terms: 9 + x = 13.820274961 Solving 9 + x = 13.820274961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 13.820274961 + -9 Combine like terms: 9 + -9 = 0 0 + x = 13.820274961 + -9 x = 13.820274961 + -9 Combine like terms: 13.820274961 + -9 = 4.820274961 x = 4.820274961 Simplifying x = 4.820274961Subproblem 2
x + 9 = -13.820274961 Simplifying x + 9 = -13.820274961 Reorder the terms: 9 + x = -13.820274961 Solving 9 + x = -13.820274961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -13.820274961 + -9 Combine like terms: 9 + -9 = 0 0 + x = -13.820274961 + -9 x = -13.820274961 + -9 Combine like terms: -13.820274961 + -9 = -22.820274961 x = -22.820274961 Simplifying x = -22.820274961Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.820274961, -22.820274961}
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