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Simplifying 0.4x2 + -36x + 405 = 0 Reorder the terms: 405 + -36x + 0.4x2 = 0 Solving 405 + -36x + 0.4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.4 the coefficient of the squared term: Divide each side by '0.4'. 1012.5 + -90x + x2 = 0 Move the constant term to the right: Add '-1012.5' to each side of the equation. 1012.5 + -90x + -1012.5 + x2 = 0 + -1012.5 Reorder the terms: 1012.5 + -1012.5 + -90x + x2 = 0 + -1012.5 Combine like terms: 1012.5 + -1012.5 = 0.0 0.0 + -90x + x2 = 0 + -1012.5 -90x + x2 = 0 + -1012.5 Combine like terms: 0 + -1012.5 = -1012.5 -90x + x2 = -1012.5 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 = -1012.5 + 2025 Reorder the terms: 2025 + -90x + x2 = -1012.5 + 2025 Combine like terms: -1012.5 + 2025 = 1012.5 2025 + -90x + x2 = 1012.5 Factor a perfect square on the left side: (x + -45)(x + -45) = 1012.5 Calculate the square root of the right side: 31.819805153 Break this problem into two subproblems by setting (x + -45) equal to 31.819805153 and -31.819805153.Subproblem 1
x + -45 = 31.819805153 Simplifying x + -45 = 31.819805153 Reorder the terms: -45 + x = 31.819805153 Solving -45 + x = 31.819805153 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 = 31.819805153 + 45 Combine like terms: -45 + 45 = 0 0 + x = 31.819805153 + 45 x = 31.819805153 + 45 Combine like terms: 31.819805153 + 45 = 76.819805153 x = 76.819805153 Simplifying x = 76.819805153Subproblem 2
x + -45 = -31.819805153 Simplifying x + -45 = -31.819805153 Reorder the terms: -45 + x = -31.819805153 Solving -45 + x = -31.819805153 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 = -31.819805153 + 45 Combine like terms: -45 + 45 = 0 0 + x = -31.819805153 + 45 x = -31.819805153 + 45 Combine like terms: -31.819805153 + 45 = 13.180194847 x = 13.180194847 Simplifying x = 13.180194847Solution
The solution to the problem is based on the solutions from the subproblems. x = {76.819805153, 13.180194847}
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