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Simplifying x2 + -18x + 75 = 0 Reorder the terms: 75 + -18x + x2 = 0 Solving 75 + -18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-75' to each side of the equation. 75 + -18x + -75 + x2 = 0 + -75 Reorder the terms: 75 + -75 + -18x + x2 = 0 + -75 Combine like terms: 75 + -75 = 0 0 + -18x + x2 = 0 + -75 -18x + x2 = 0 + -75 Combine like terms: 0 + -75 = -75 -18x + x2 = -75 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 = -75 + 81 Reorder the terms: 81 + -18x + x2 = -75 + 81 Combine like terms: -75 + 81 = 6 81 + -18x + x2 = 6 Factor a perfect square on the left side: (x + -9)(x + -9) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + -9) equal to 2.449489743 and -2.449489743.Subproblem 1
x + -9 = 2.449489743 Simplifying x + -9 = 2.449489743 Reorder the terms: -9 + x = 2.449489743 Solving -9 + x = 2.449489743 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 = 2.449489743 + 9 Combine like terms: -9 + 9 = 0 0 + x = 2.449489743 + 9 x = 2.449489743 + 9 Combine like terms: 2.449489743 + 9 = 11.449489743 x = 11.449489743 Simplifying x = 11.449489743Subproblem 2
x + -9 = -2.449489743 Simplifying x + -9 = -2.449489743 Reorder the terms: -9 + x = -2.449489743 Solving -9 + x = -2.449489743 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 = -2.449489743 + 9 Combine like terms: -9 + 9 = 0 0 + x = -2.449489743 + 9 x = -2.449489743 + 9 Combine like terms: -2.449489743 + 9 = 6.550510257 x = 6.550510257 Simplifying x = 6.550510257Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.449489743, 6.550510257}
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