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Simplifying x2 + 18x + -270 = 0 Reorder the terms: -270 + 18x + x2 = 0 Solving -270 + 18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '270' to each side of the equation. -270 + 18x + 270 + x2 = 0 + 270 Reorder the terms: -270 + 270 + 18x + x2 = 0 + 270 Combine like terms: -270 + 270 = 0 0 + 18x + x2 = 0 + 270 18x + x2 = 0 + 270 Combine like terms: 0 + 270 = 270 18x + x2 = 270 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 = 270 + 81 Reorder the terms: 81 + 18x + x2 = 270 + 81 Combine like terms: 270 + 81 = 351 81 + 18x + x2 = 351 Factor a perfect square on the left side: (x + 9)(x + 9) = 351 Calculate the square root of the right side: 18.734993995 Break this problem into two subproblems by setting (x + 9) equal to 18.734993995 and -18.734993995.Subproblem 1
x + 9 = 18.734993995 Simplifying x + 9 = 18.734993995 Reorder the terms: 9 + x = 18.734993995 Solving 9 + x = 18.734993995 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 = 18.734993995 + -9 Combine like terms: 9 + -9 = 0 0 + x = 18.734993995 + -9 x = 18.734993995 + -9 Combine like terms: 18.734993995 + -9 = 9.734993995 x = 9.734993995 Simplifying x = 9.734993995Subproblem 2
x + 9 = -18.734993995 Simplifying x + 9 = -18.734993995 Reorder the terms: 9 + x = -18.734993995 Solving 9 + x = -18.734993995 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 = -18.734993995 + -9 Combine like terms: 9 + -9 = 0 0 + x = -18.734993995 + -9 x = -18.734993995 + -9 Combine like terms: -18.734993995 + -9 = -27.734993995 x = -27.734993995 Simplifying x = -27.734993995Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.734993995, -27.734993995}
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