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Simplifying x2 + 18x = 300 Reorder the terms: 18x + x2 = 300 Solving 18x + x2 = 300 Solving for variable 'x'. Reorder the terms: -300 + 18x + x2 = 300 + -300 Combine like terms: 300 + -300 = 0 -300 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '300' to each side of the equation. -300 + 18x + 300 + x2 = 0 + 300 Reorder the terms: -300 + 300 + 18x + x2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + 18x + x2 = 0 + 300 18x + x2 = 0 + 300 Combine like terms: 0 + 300 = 300 18x + x2 = 300 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 = 300 + 81 Reorder the terms: 81 + 18x + x2 = 300 + 81 Combine like terms: 300 + 81 = 381 81 + 18x + x2 = 381 Factor a perfect square on the left side: (x + 9)(x + 9) = 381 Calculate the square root of the right side: 19.519221296 Break this problem into two subproblems by setting (x + 9) equal to 19.519221296 and -19.519221296.Subproblem 1
x + 9 = 19.519221296 Simplifying x + 9 = 19.519221296 Reorder the terms: 9 + x = 19.519221296 Solving 9 + x = 19.519221296 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 = 19.519221296 + -9 Combine like terms: 9 + -9 = 0 0 + x = 19.519221296 + -9 x = 19.519221296 + -9 Combine like terms: 19.519221296 + -9 = 10.519221296 x = 10.519221296 Simplifying x = 10.519221296Subproblem 2
x + 9 = -19.519221296 Simplifying x + 9 = -19.519221296 Reorder the terms: 9 + x = -19.519221296 Solving 9 + x = -19.519221296 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 = -19.519221296 + -9 Combine like terms: 9 + -9 = 0 0 + x = -19.519221296 + -9 x = -19.519221296 + -9 Combine like terms: -19.519221296 + -9 = -28.519221296 x = -28.519221296 Simplifying x = -28.519221296Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.519221296, -28.519221296}
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