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Simplifying 0.02x2 + 0.5x + -4 = 0 Reorder the terms: -4 + 0.5x + 0.02x2 = 0 Solving -4 + 0.5x + 0.02x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.02 the coefficient of the squared term: Divide each side by '0.02'. -200 + 25x + x2 = 0 Move the constant term to the right: Add '200' to each side of the equation. -200 + 25x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + 25x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + 25x + x2 = 0 + 200 25x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 25x + x2 = 200 The x term is 25x. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25x + 156.25 + x2 = 200 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 200 + 156.25 Combine like terms: 200 + 156.25 = 356.25 156.25 + 25x + x2 = 356.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 356.25 Calculate the square root of the right side: 18.874586088 Break this problem into two subproblems by setting (x + 12.5) equal to 18.874586088 and -18.874586088.Subproblem 1
x + 12.5 = 18.874586088 Simplifying x + 12.5 = 18.874586088 Reorder the terms: 12.5 + x = 18.874586088 Solving 12.5 + x = 18.874586088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = 18.874586088 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 18.874586088 + -12.5 x = 18.874586088 + -12.5 Combine like terms: 18.874586088 + -12.5 = 6.374586088 x = 6.374586088 Simplifying x = 6.374586088Subproblem 2
x + 12.5 = -18.874586088 Simplifying x + 12.5 = -18.874586088 Reorder the terms: 12.5 + x = -18.874586088 Solving 12.5 + x = -18.874586088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = -18.874586088 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -18.874586088 + -12.5 x = -18.874586088 + -12.5 Combine like terms: -18.874586088 + -12.5 = -31.374586088 x = -31.374586088 Simplifying x = -31.374586088Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.374586088, -31.374586088}
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