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Simplifying x2 + 18x + 53 = 594 Reorder the terms: 53 + 18x + x2 = 594 Solving 53 + 18x + x2 = 594 Solving for variable 'x'. Reorder the terms: 53 + -594 + 18x + x2 = 594 + -594 Combine like terms: 53 + -594 = -541 -541 + 18x + x2 = 594 + -594 Combine like terms: 594 + -594 = 0 -541 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '541' to each side of the equation. -541 + 18x + 541 + x2 = 0 + 541 Reorder the terms: -541 + 541 + 18x + x2 = 0 + 541 Combine like terms: -541 + 541 = 0 0 + 18x + x2 = 0 + 541 18x + x2 = 0 + 541 Combine like terms: 0 + 541 = 541 18x + x2 = 541 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 = 541 + 81 Reorder the terms: 81 + 18x + x2 = 541 + 81 Combine like terms: 541 + 81 = 622 81 + 18x + x2 = 622 Factor a perfect square on the left side: (x + 9)(x + 9) = 622 Calculate the square root of the right side: 24.939927827 Break this problem into two subproblems by setting (x + 9) equal to 24.939927827 and -24.939927827.Subproblem 1
x + 9 = 24.939927827 Simplifying x + 9 = 24.939927827 Reorder the terms: 9 + x = 24.939927827 Solving 9 + x = 24.939927827 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 = 24.939927827 + -9 Combine like terms: 9 + -9 = 0 0 + x = 24.939927827 + -9 x = 24.939927827 + -9 Combine like terms: 24.939927827 + -9 = 15.939927827 x = 15.939927827 Simplifying x = 15.939927827Subproblem 2
x + 9 = -24.939927827 Simplifying x + 9 = -24.939927827 Reorder the terms: 9 + x = -24.939927827 Solving 9 + x = -24.939927827 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 = -24.939927827 + -9 Combine like terms: 9 + -9 = 0 0 + x = -24.939927827 + -9 x = -24.939927827 + -9 Combine like terms: -24.939927827 + -9 = -33.939927827 x = -33.939927827 Simplifying x = -33.939927827Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.939927827, -33.939927827}
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