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Simplifying x2 + 18x + 81 = 525 Reorder the terms: 81 + 18x + x2 = 525 Solving 81 + 18x + x2 = 525 Solving for variable 'x'. Reorder the terms: 81 + -525 + 18x + x2 = 525 + -525 Combine like terms: 81 + -525 = -444 -444 + 18x + x2 = 525 + -525 Combine like terms: 525 + -525 = 0 -444 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '444' to each side of the equation. -444 + 18x + 444 + x2 = 0 + 444 Reorder the terms: -444 + 444 + 18x + x2 = 0 + 444 Combine like terms: -444 + 444 = 0 0 + 18x + x2 = 0 + 444 18x + x2 = 0 + 444 Combine like terms: 0 + 444 = 444 18x + x2 = 444 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 = 444 + 81 Reorder the terms: 81 + 18x + x2 = 444 + 81 Combine like terms: 444 + 81 = 525 81 + 18x + x2 = 525 Factor a perfect square on the left side: (x + 9)(x + 9) = 525 Calculate the square root of the right side: 22.912878475 Break this problem into two subproblems by setting (x + 9) equal to 22.912878475 and -22.912878475.Subproblem 1
x + 9 = 22.912878475 Simplifying x + 9 = 22.912878475 Reorder the terms: 9 + x = 22.912878475 Solving 9 + x = 22.912878475 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 = 22.912878475 + -9 Combine like terms: 9 + -9 = 0 0 + x = 22.912878475 + -9 x = 22.912878475 + -9 Combine like terms: 22.912878475 + -9 = 13.912878475 x = 13.912878475 Simplifying x = 13.912878475Subproblem 2
x + 9 = -22.912878475 Simplifying x + 9 = -22.912878475 Reorder the terms: 9 + x = -22.912878475 Solving 9 + x = -22.912878475 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 = -22.912878475 + -9 Combine like terms: 9 + -9 = 0 0 + x = -22.912878475 + -9 x = -22.912878475 + -9 Combine like terms: -22.912878475 + -9 = -31.912878475 x = -31.912878475 Simplifying x = -31.912878475Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.912878475, -31.912878475}
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