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Simplifying 36x + -0.8x2 + -405 = 0 Reorder the terms: -405 + 36x + -0.8x2 = 0 Solving -405 + 36x + -0.8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.8 the coefficient of the squared term: Divide each side by '-0.8'. 506.25 + -45x + x2 = 0 Move the constant term to the right: Add '-506.25' to each side of the equation. 506.25 + -45x + -506.25 + x2 = 0 + -506.25 Reorder the terms: 506.25 + -506.25 + -45x + x2 = 0 + -506.25 Combine like terms: 506.25 + -506.25 = 0.00 0.00 + -45x + x2 = 0 + -506.25 -45x + x2 = 0 + -506.25 Combine like terms: 0 + -506.25 = -506.25 -45x + x2 = -506.25 The x term is -45x. Take half its coefficient (-22.5). Square it (506.25) and add it to both sides. Add '506.25' to each side of the equation. -45x + 506.25 + x2 = -506.25 + 506.25 Reorder the terms: 506.25 + -45x + x2 = -506.25 + 506.25 Combine like terms: -506.25 + 506.25 = 0.00 506.25 + -45x + x2 = 0.00 Factor a perfect square on the left side: (x + -22.5)(x + -22.5) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (x + -22.5) equal to 0.00 and 0.00.Subproblem 1
x + -22.5 = 0.00 Simplifying x + -22.5 = 0.00 Reorder the terms: -22.5 + x = 0.00 Solving -22.5 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.5' to each side of the equation. -22.5 + 22.5 + x = 0.00 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = 0.00 + 22.5 x = 0.00 + 22.5 Combine like terms: 0.00 + 22.5 = 22.5 x = 22.5 Simplifying x = 22.5Subproblem 2
x + -22.5 = 0.00 Simplifying x + -22.5 = 0.00 Reorder the terms: -22.5 + x = 0.00 Solving -22.5 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.5' to each side of the equation. -22.5 + 22.5 + x = 0.00 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = 0.00 + 22.5 x = 0.00 + 22.5 Combine like terms: 0.00 + 22.5 = 22.5 x = 22.5 Simplifying x = 22.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.5, 22.5}
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