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Simplifying (x + -2)(x + 2) + 17 = 18x Reorder the terms: (-2 + x)(x + 2) + 17 = 18x Reorder the terms: (-2 + x)(2 + x) + 17 = 18x Multiply (-2 + x) * (2 + x) (-2(2 + x) + x(2 + x)) + 17 = 18x ((2 * -2 + x * -2) + x(2 + x)) + 17 = 18x ((-4 + -2x) + x(2 + x)) + 17 = 18x (-4 + -2x + (2 * x + x * x)) + 17 = 18x (-4 + -2x + (2x + x2)) + 17 = 18x Combine like terms: -2x + 2x = 0 (-4 + 0 + x2) + 17 = 18x (-4 + x2) + 17 = 18x Reorder the terms: -4 + 17 + x2 = 18x Combine like terms: -4 + 17 = 13 13 + x2 = 18x Solving 13 + x2 = 18x Solving for variable 'x'. Reorder the terms: 13 + -18x + x2 = 18x + -18x Combine like terms: 18x + -18x = 0 13 + -18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + -18x + -13 + x2 = 0 + -13 Reorder the terms: 13 + -13 + -18x + x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -18x + x2 = 0 + -13 -18x + x2 = 0 + -13 Combine like terms: 0 + -13 = -13 -18x + x2 = -13 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 = -13 + 81 Reorder the terms: 81 + -18x + x2 = -13 + 81 Combine like terms: -13 + 81 = 68 81 + -18x + x2 = 68 Factor a perfect square on the left side: (x + -9)(x + -9) = 68 Calculate the square root of the right side: 8.246211251 Break this problem into two subproblems by setting (x + -9) equal to 8.246211251 and -8.246211251.Subproblem 1
x + -9 = 8.246211251 Simplifying x + -9 = 8.246211251 Reorder the terms: -9 + x = 8.246211251 Solving -9 + x = 8.246211251 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 = 8.246211251 + 9 Combine like terms: -9 + 9 = 0 0 + x = 8.246211251 + 9 x = 8.246211251 + 9 Combine like terms: 8.246211251 + 9 = 17.246211251 x = 17.246211251 Simplifying x = 17.246211251Subproblem 2
x + -9 = -8.246211251 Simplifying x + -9 = -8.246211251 Reorder the terms: -9 + x = -8.246211251 Solving -9 + x = -8.246211251 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 = -8.246211251 + 9 Combine like terms: -9 + 9 = 0 0 + x = -8.246211251 + 9 x = -8.246211251 + 9 Combine like terms: -8.246211251 + 9 = 0.753788749 x = 0.753788749 Simplifying x = 0.753788749Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.246211251, 0.753788749}
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