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Simplifying x(90 + -1x) = 18 (90 * x + -1x * x) = 18 (90x + -1x2) = 18 Solving 90x + -1x2 = 18 Solving for variable 'x'. Reorder the terms: -18 + 90x + -1x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + 90x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 18 + -90x + x2 = 0 Move the constant term to the right: Add '-18' to each side of the equation. 18 + -90x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + -90x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -90x + x2 = 0 + -18 -90x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 -90x + x2 = -18 The x term is -90x. Take half its coefficient (-45). Square it (2025) and add it to both sides. Add '2025' to each side of the equation. -90x + 2025 + x2 = -18 + 2025 Reorder the terms: 2025 + -90x + x2 = -18 + 2025 Combine like terms: -18 + 2025 = 2007 2025 + -90x + x2 = 2007 Factor a perfect square on the left side: (x + -45)(x + -45) = 2007 Calculate the square root of the right side: 44.799553569 Break this problem into two subproblems by setting (x + -45) equal to 44.799553569 and -44.799553569.Subproblem 1
x + -45 = 44.799553569 Simplifying x + -45 = 44.799553569 Reorder the terms: -45 + x = 44.799553569 Solving -45 + x = 44.799553569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + x = 44.799553569 + 45 Combine like terms: -45 + 45 = 0 0 + x = 44.799553569 + 45 x = 44.799553569 + 45 Combine like terms: 44.799553569 + 45 = 89.799553569 x = 89.799553569 Simplifying x = 89.799553569Subproblem 2
x + -45 = -44.799553569 Simplifying x + -45 = -44.799553569 Reorder the terms: -45 + x = -44.799553569 Solving -45 + x = -44.799553569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + x = -44.799553569 + 45 Combine like terms: -45 + 45 = 0 0 + x = -44.799553569 + 45 x = -44.799553569 + 45 Combine like terms: -44.799553569 + 45 = 0.200446431 x = 0.200446431 Simplifying x = 0.200446431Solution
The solution to the problem is based on the solutions from the subproblems. x = {89.799553569, 0.200446431}
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