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Simplifying x2 + 18x + 77 + -4 = 187 Reorder the terms: 77 + -4 + 18x + x2 = 187 Combine like terms: 77 + -4 = 73 73 + 18x + x2 = 187 Solving 73 + 18x + x2 = 187 Solving for variable 'x'. Reorder the terms: 73 + -187 + 18x + x2 = 187 + -187 Combine like terms: 73 + -187 = -114 -114 + 18x + x2 = 187 + -187 Combine like terms: 187 + -187 = 0 -114 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '114' to each side of the equation. -114 + 18x + 114 + x2 = 0 + 114 Reorder the terms: -114 + 114 + 18x + x2 = 0 + 114 Combine like terms: -114 + 114 = 0 0 + 18x + x2 = 0 + 114 18x + x2 = 0 + 114 Combine like terms: 0 + 114 = 114 18x + x2 = 114 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 = 114 + 81 Reorder the terms: 81 + 18x + x2 = 114 + 81 Combine like terms: 114 + 81 = 195 81 + 18x + x2 = 195 Factor a perfect square on the left side: (x + 9)(x + 9) = 195 Calculate the square root of the right side: 13.964240044 Break this problem into two subproblems by setting (x + 9) equal to 13.964240044 and -13.964240044.Subproblem 1
x + 9 = 13.964240044 Simplifying x + 9 = 13.964240044 Reorder the terms: 9 + x = 13.964240044 Solving 9 + x = 13.964240044 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 = 13.964240044 + -9 Combine like terms: 9 + -9 = 0 0 + x = 13.964240044 + -9 x = 13.964240044 + -9 Combine like terms: 13.964240044 + -9 = 4.964240044 x = 4.964240044 Simplifying x = 4.964240044Subproblem 2
x + 9 = -13.964240044 Simplifying x + 9 = -13.964240044 Reorder the terms: 9 + x = -13.964240044 Solving 9 + x = -13.964240044 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 = -13.964240044 + -9 Combine like terms: 9 + -9 = 0 0 + x = -13.964240044 + -9 x = -13.964240044 + -9 Combine like terms: -13.964240044 + -9 = -22.964240044 x = -22.964240044 Simplifying x = -22.964240044Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.964240044, -22.964240044}
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