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Simplifying 0.5x2 + -18x + 27 = 0 Reorder the terms: 27 + -18x + 0.5x2 = 0 Solving 27 + -18x + 0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 54 + -36x + x2 = 0 Move the constant term to the right: Add '-54' to each side of the equation. 54 + -36x + -54 + x2 = 0 + -54 Reorder the terms: 54 + -54 + -36x + x2 = 0 + -54 Combine like terms: 54 + -54 = 0 0 + -36x + x2 = 0 + -54 -36x + x2 = 0 + -54 Combine like terms: 0 + -54 = -54 -36x + x2 = -54 The x term is -36x. Take half its coefficient (-18). Square it (324) and add it to both sides. Add '324' to each side of the equation. -36x + 324 + x2 = -54 + 324 Reorder the terms: 324 + -36x + x2 = -54 + 324 Combine like terms: -54 + 324 = 270 324 + -36x + x2 = 270 Factor a perfect square on the left side: (x + -18)(x + -18) = 270 Calculate the square root of the right side: 16.431676725 Break this problem into two subproblems by setting (x + -18) equal to 16.431676725 and -16.431676725.Subproblem 1
x + -18 = 16.431676725 Simplifying x + -18 = 16.431676725 Reorder the terms: -18 + x = 16.431676725 Solving -18 + x = 16.431676725 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = 16.431676725 + 18 Combine like terms: -18 + 18 = 0 0 + x = 16.431676725 + 18 x = 16.431676725 + 18 Combine like terms: 16.431676725 + 18 = 34.431676725 x = 34.431676725 Simplifying x = 34.431676725Subproblem 2
x + -18 = -16.431676725 Simplifying x + -18 = -16.431676725 Reorder the terms: -18 + x = -16.431676725 Solving -18 + x = -16.431676725 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = -16.431676725 + 18 Combine like terms: -18 + 18 = 0 0 + x = -16.431676725 + 18 x = -16.431676725 + 18 Combine like terms: -16.431676725 + 18 = 1.568323275 x = 1.568323275 Simplifying x = 1.568323275Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.431676725, 1.568323275}
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