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Simplifying 0.5x(18 + -1x) = 5.2 (18 * 0.5x + -1x * 0.5x) = 5.2 (9x + -0.5x2) = 5.2 Solving 9x + -0.5x2 = 5.2 Solving for variable 'x'. Reorder the terms: -5.2 + 9x + -0.5x2 = 5.2 + -5.2 Combine like terms: 5.2 + -5.2 = 0.0 -5.2 + 9x + -0.5x2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. 10.4 + -18x + x2 = 0 Move the constant term to the right: Add '-10.4' to each side of the equation. 10.4 + -18x + -10.4 + x2 = 0 + -10.4 Reorder the terms: 10.4 + -10.4 + -18x + x2 = 0 + -10.4 Combine like terms: 10.4 + -10.4 = 0.0 0.0 + -18x + x2 = 0 + -10.4 -18x + x2 = 0 + -10.4 Combine like terms: 0 + -10.4 = -10.4 -18x + x2 = -10.4 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 = -10.4 + 81 Reorder the terms: 81 + -18x + x2 = -10.4 + 81 Combine like terms: -10.4 + 81 = 70.6 81 + -18x + x2 = 70.6 Factor a perfect square on the left side: (x + -9)(x + -9) = 70.6 Calculate the square root of the right side: 8.402380615 Break this problem into two subproblems by setting (x + -9) equal to 8.402380615 and -8.402380615.Subproblem 1
x + -9 = 8.402380615 Simplifying x + -9 = 8.402380615 Reorder the terms: -9 + x = 8.402380615 Solving -9 + x = 8.402380615 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 = 8.402380615 + 9 Combine like terms: -9 + 9 = 0 0 + x = 8.402380615 + 9 x = 8.402380615 + 9 Combine like terms: 8.402380615 + 9 = 17.402380615 x = 17.402380615 Simplifying x = 17.402380615Subproblem 2
x + -9 = -8.402380615 Simplifying x + -9 = -8.402380615 Reorder the terms: -9 + x = -8.402380615 Solving -9 + x = -8.402380615 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 = -8.402380615 + 9 Combine like terms: -9 + 9 = 0 0 + x = -8.402380615 + 9 x = -8.402380615 + 9 Combine like terms: -8.402380615 + 9 = 0.597619385 x = 0.597619385 Simplifying x = 0.597619385Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.402380615, 0.597619385}
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