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Simplifying x2 + -18x + 30 = 0 Reorder the terms: 30 + -18x + x2 = 0 Solving 30 + -18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + -18x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + -18x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -18x + x2 = 0 + -30 -18x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 -18x + x2 = -30 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 = -30 + 81 Reorder the terms: 81 + -18x + x2 = -30 + 81 Combine like terms: -30 + 81 = 51 81 + -18x + x2 = 51 Factor a perfect square on the left side: (x + -9)(x + -9) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (x + -9) equal to 7.141428429 and -7.141428429.Subproblem 1
x + -9 = 7.141428429 Simplifying x + -9 = 7.141428429 Reorder the terms: -9 + x = 7.141428429 Solving -9 + x = 7.141428429 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 = 7.141428429 + 9 Combine like terms: -9 + 9 = 0 0 + x = 7.141428429 + 9 x = 7.141428429 + 9 Combine like terms: 7.141428429 + 9 = 16.141428429 x = 16.141428429 Simplifying x = 16.141428429Subproblem 2
x + -9 = -7.141428429 Simplifying x + -9 = -7.141428429 Reorder the terms: -9 + x = -7.141428429 Solving -9 + x = -7.141428429 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 = -7.141428429 + 9 Combine like terms: -9 + 9 = 0 0 + x = -7.141428429 + 9 x = -7.141428429 + 9 Combine like terms: -7.141428429 + 9 = 1.858571571 x = 1.858571571 Simplifying x = 1.858571571Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.141428429, 1.858571571}
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