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Simplifying x2 + 18x + 69 = 3 Reorder the terms: 69 + 18x + x2 = 3 Solving 69 + 18x + x2 = 3 Solving for variable 'x'. Reorder the terms: 69 + -3 + 18x + x2 = 3 + -3 Combine like terms: 69 + -3 = 66 66 + 18x + x2 = 3 + -3 Combine like terms: 3 + -3 = 0 66 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-66' to each side of the equation. 66 + 18x + -66 + x2 = 0 + -66 Reorder the terms: 66 + -66 + 18x + x2 = 0 + -66 Combine like terms: 66 + -66 = 0 0 + 18x + x2 = 0 + -66 18x + x2 = 0 + -66 Combine like terms: 0 + -66 = -66 18x + x2 = -66 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 = -66 + 81 Reorder the terms: 81 + 18x + x2 = -66 + 81 Combine like terms: -66 + 81 = 15 81 + 18x + x2 = 15 Factor a perfect square on the left side: (x + 9)(x + 9) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (x + 9) equal to 3.872983346 and -3.872983346.Subproblem 1
x + 9 = 3.872983346 Simplifying x + 9 = 3.872983346 Reorder the terms: 9 + x = 3.872983346 Solving 9 + x = 3.872983346 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 = 3.872983346 + -9 Combine like terms: 9 + -9 = 0 0 + x = 3.872983346 + -9 x = 3.872983346 + -9 Combine like terms: 3.872983346 + -9 = -5.127016654 x = -5.127016654 Simplifying x = -5.127016654Subproblem 2
x + 9 = -3.872983346 Simplifying x + 9 = -3.872983346 Reorder the terms: 9 + x = -3.872983346 Solving 9 + x = -3.872983346 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 = -3.872983346 + -9 Combine like terms: 9 + -9 = 0 0 + x = -3.872983346 + -9 x = -3.872983346 + -9 Combine like terms: -3.872983346 + -9 = -12.872983346 x = -12.872983346 Simplifying x = -12.872983346Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.127016654, -12.872983346}
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