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Simplifying 0.2x2 + -9x + 0.2 = 0 Reorder the terms: 0.2 + -9x + 0.2x2 = 0 Solving 0.2 + -9x + 0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. 1 + -45x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -45x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -45x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -45x + x2 = 0 + -1 -45x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -45x + x2 = -1 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 = -1 + 506.25 Reorder the terms: 506.25 + -45x + x2 = -1 + 506.25 Combine like terms: -1 + 506.25 = 505.25 506.25 + -45x + x2 = 505.25 Factor a perfect square on the left side: (x + -22.5)(x + -22.5) = 505.25 Calculate the square root of the right side: 22.477766793 Break this problem into two subproblems by setting (x + -22.5) equal to 22.477766793 and -22.477766793.Subproblem 1
x + -22.5 = 22.477766793 Simplifying x + -22.5 = 22.477766793 Reorder the terms: -22.5 + x = 22.477766793 Solving -22.5 + x = 22.477766793 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 = 22.477766793 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = 22.477766793 + 22.5 x = 22.477766793 + 22.5 Combine like terms: 22.477766793 + 22.5 = 44.977766793 x = 44.977766793 Simplifying x = 44.977766793Subproblem 2
x + -22.5 = -22.477766793 Simplifying x + -22.5 = -22.477766793 Reorder the terms: -22.5 + x = -22.477766793 Solving -22.5 + x = -22.477766793 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 = -22.477766793 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = -22.477766793 + 22.5 x = -22.477766793 + 22.5 Combine like terms: -22.477766793 + 22.5 = 0.022233207 x = 0.022233207 Simplifying x = 0.022233207Solution
The solution to the problem is based on the solutions from the subproblems. x = {44.977766793, 0.022233207}
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