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Simplifying -18x + 0.5x2 = -144 Solving -18x + 0.5x2 = -144 Solving for variable 'x'. Reorder the terms: 144 + -18x + 0.5x2 = -144 + 144 Combine like terms: -144 + 144 = 0 144 + -18x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 288 + -36x + x2 = 0 Move the constant term to the right: Add '-288' to each side of the equation. 288 + -36x + -288 + x2 = 0 + -288 Reorder the terms: 288 + -288 + -36x + x2 = 0 + -288 Combine like terms: 288 + -288 = 0 0 + -36x + x2 = 0 + -288 -36x + x2 = 0 + -288 Combine like terms: 0 + -288 = -288 -36x + x2 = -288 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 = -288 + 324 Reorder the terms: 324 + -36x + x2 = -288 + 324 Combine like terms: -288 + 324 = 36 324 + -36x + x2 = 36 Factor a perfect square on the left side: (x + -18)(x + -18) = 36 Calculate the square root of the right side: 6 Break this problem into two subproblems by setting (x + -18) equal to 6 and -6.Subproblem 1
x + -18 = 6 Simplifying x + -18 = 6 Reorder the terms: -18 + x = 6 Solving -18 + x = 6 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 = 6 + 18 Combine like terms: -18 + 18 = 0 0 + x = 6 + 18 x = 6 + 18 Combine like terms: 6 + 18 = 24 x = 24 Simplifying x = 24Subproblem 2
x + -18 = -6 Simplifying x + -18 = -6 Reorder the terms: -18 + x = -6 Solving -18 + x = -6 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 = -6 + 18 Combine like terms: -18 + 18 = 0 0 + x = -6 + 18 x = -6 + 18 Combine like terms: -6 + 18 = 12 x = 12 Simplifying x = 12Solution
The solution to the problem is based on the solutions from the subproblems. x = {24, 12}
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