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Simplifying x2 + 18x = 389 Reorder the terms: 18x + x2 = 389 Solving 18x + x2 = 389 Solving for variable 'x'. Reorder the terms: -389 + 18x + x2 = 389 + -389 Combine like terms: 389 + -389 = 0 -389 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '389' to each side of the equation. -389 + 18x + 389 + x2 = 0 + 389 Reorder the terms: -389 + 389 + 18x + x2 = 0 + 389 Combine like terms: -389 + 389 = 0 0 + 18x + x2 = 0 + 389 18x + x2 = 0 + 389 Combine like terms: 0 + 389 = 389 18x + x2 = 389 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 = 389 + 81 Reorder the terms: 81 + 18x + x2 = 389 + 81 Combine like terms: 389 + 81 = 470 81 + 18x + x2 = 470 Factor a perfect square on the left side: (x + 9)(x + 9) = 470 Calculate the square root of the right side: 21.679483389 Break this problem into two subproblems by setting (x + 9) equal to 21.679483389 and -21.679483389.Subproblem 1
x + 9 = 21.679483389 Simplifying x + 9 = 21.679483389 Reorder the terms: 9 + x = 21.679483389 Solving 9 + x = 21.679483389 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 = 21.679483389 + -9 Combine like terms: 9 + -9 = 0 0 + x = 21.679483389 + -9 x = 21.679483389 + -9 Combine like terms: 21.679483389 + -9 = 12.679483389 x = 12.679483389 Simplifying x = 12.679483389Subproblem 2
x + 9 = -21.679483389 Simplifying x + 9 = -21.679483389 Reorder the terms: 9 + x = -21.679483389 Solving 9 + x = -21.679483389 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 = -21.679483389 + -9 Combine like terms: 9 + -9 = 0 0 + x = -21.679483389 + -9 x = -21.679483389 + -9 Combine like terms: -21.679483389 + -9 = -30.679483389 x = -30.679483389 Simplifying x = -30.679483389Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.679483389, -30.679483389}
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