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Simplifying 0 = (x2) + (90x) + -36 0 = x2 + (90x) + -36 Reorder the terms: 0 = -36 + (90x) + x2 Solving 0 = -36 + (90x) + x2 Solving for variable 'x'. Combine like terms: 0 + 36 = 36 36 + (-90x) + -1x2 = -36 + (90x) + x2 + 36 + (-90x) + -1x2 Reorder the terms: 36 + (-90x) + -1x2 = -36 + 36 + (90x) + (-90x) + x2 + -1x2 Combine like terms: -36 + 36 = 0 36 + (-90x) + -1x2 = 0 + (90x) + (-90x) + x2 + -1x2 36 + (-90x) + -1x2 = (90x) + (-90x) + x2 + -1x2 Combine like terms: (90x) + (-90x) = 0 36 + (-90x) + -1x2 = 0 + x2 + -1x2 36 + (-90x) + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 36 + (-90x) + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -36 + (90x) + x2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + (90x) + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + (90x) + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + (90x) + x2 = 0 + 36 (90x) + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 (90x) + x2 = 36 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 = 36 + 2025 Reorder the terms: 2025 + (90x) + x2 = 36 + 2025 Combine like terms: 36 + 2025 = 2061 2025 + (90x) + x2 = 2061 Factor a perfect square on the left side: (x + 45)(x + 45) = 2061 Calculate the square root of the right side: 45.398237851 Break this problem into two subproblems by setting (x + 45) equal to 45.398237851 and -45.398237851.Subproblem 1
x + 45 = 45.398237851 Simplifying x + 45 = 45.398237851 Reorder the terms: 45 + x = 45.398237851 Solving 45 + x = 45.398237851 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 = 45.398237851 + -45 Combine like terms: 45 + -45 = 0 0 + x = 45.398237851 + -45 x = 45.398237851 + -45 Combine like terms: 45.398237851 + -45 = 0.398237851 x = 0.398237851 Simplifying x = 0.398237851Subproblem 2
x + 45 = -45.398237851 Simplifying x + 45 = -45.398237851 Reorder the terms: 45 + x = -45.398237851 Solving 45 + x = -45.398237851 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 = -45.398237851 + -45 Combine like terms: 45 + -45 = 0 0 + x = -45.398237851 + -45 x = -45.398237851 + -45 Combine like terms: -45.398237851 + -45 = -90.398237851 x = -90.398237851 Simplifying x = -90.398237851Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.398237851, -90.398237851}
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