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Simplifying 0 = x2 + -90x + -1800 Reorder the terms: 0 = -1800 + -90x + x2 Solving 0 = -1800 + -90x + x2 Solving for variable 'x'. Combine like terms: 0 + 1800 = 1800 1800 + 90x + -1x2 = -1800 + -90x + x2 + 1800 + 90x + -1x2 Reorder the terms: 1800 + 90x + -1x2 = -1800 + 1800 + -90x + 90x + x2 + -1x2 Combine like terms: -1800 + 1800 = 0 1800 + 90x + -1x2 = 0 + -90x + 90x + x2 + -1x2 1800 + 90x + -1x2 = -90x + 90x + x2 + -1x2 Combine like terms: -90x + 90x = 0 1800 + 90x + -1x2 = 0 + x2 + -1x2 1800 + 90x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 1800 + 90x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1800 + -90x + x2 = 0 Move the constant term to the right: Add '1800' to each side of the equation. -1800 + -90x + 1800 + x2 = 0 + 1800 Reorder the terms: -1800 + 1800 + -90x + x2 = 0 + 1800 Combine like terms: -1800 + 1800 = 0 0 + -90x + x2 = 0 + 1800 -90x + x2 = 0 + 1800 Combine like terms: 0 + 1800 = 1800 -90x + x2 = 1800 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 = 1800 + 2025 Reorder the terms: 2025 + -90x + x2 = 1800 + 2025 Combine like terms: 1800 + 2025 = 3825 2025 + -90x + x2 = 3825 Factor a perfect square on the left side: (x + -45)(x + -45) = 3825 Calculate the square root of the right side: 61.846584384 Break this problem into two subproblems by setting (x + -45) equal to 61.846584384 and -61.846584384.Subproblem 1
x + -45 = 61.846584384 Simplifying x + -45 = 61.846584384 Reorder the terms: -45 + x = 61.846584384 Solving -45 + x = 61.846584384 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 = 61.846584384 + 45 Combine like terms: -45 + 45 = 0 0 + x = 61.846584384 + 45 x = 61.846584384 + 45 Combine like terms: 61.846584384 + 45 = 106.846584384 x = 106.846584384 Simplifying x = 106.846584384Subproblem 2
x + -45 = -61.846584384 Simplifying x + -45 = -61.846584384 Reorder the terms: -45 + x = -61.846584384 Solving -45 + x = -61.846584384 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 = -61.846584384 + 45 Combine like terms: -45 + 45 = 0 0 + x = -61.846584384 + 45 x = -61.846584384 + 45 Combine like terms: -61.846584384 + 45 = -16.846584384 x = -16.846584384 Simplifying x = -16.846584384Solution
The solution to the problem is based on the solutions from the subproblems. x = {106.846584384, -16.846584384}
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