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Simplifying 0.085x2 + -5x + 40 = 0 Reorder the terms: 40 + -5x + 0.085x2 = 0 Solving 40 + -5x + 0.085x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.085 the coefficient of the squared term: Divide each side by '0.085'. 470.5882353 + -58.82352941x + x2 = 0 Move the constant term to the right: Add '-470.5882353' to each side of the equation. 470.5882353 + -58.82352941x + -470.5882353 + x2 = 0 + -470.5882353 Reorder the terms: 470.5882353 + -470.5882353 + -58.82352941x + x2 = 0 + -470.5882353 Combine like terms: 470.5882353 + -470.5882353 = 0.0000000 0.0000000 + -58.82352941x + x2 = 0 + -470.5882353 -58.82352941x + x2 = 0 + -470.5882353 Combine like terms: 0 + -470.5882353 = -470.5882353 -58.82352941x + x2 = -470.5882353 The x term is -58.82352941x. Take half its coefficient (-29.41176471). Square it (865.0519034) and add it to both sides. Add '865.0519034' to each side of the equation. -58.82352941x + 865.0519034 + x2 = -470.5882353 + 865.0519034 Reorder the terms: 865.0519034 + -58.82352941x + x2 = -470.5882353 + 865.0519034 Combine like terms: -470.5882353 + 865.0519034 = 394.4636681 865.0519034 + -58.82352941x + x2 = 394.4636681 Factor a perfect square on the left side: (x + -29.41176471)(x + -29.41176471) = 394.4636681 Calculate the square root of the right side: 19.861109438 Break this problem into two subproblems by setting (x + -29.41176471) equal to 19.861109438 and -19.861109438.Subproblem 1
x + -29.41176471 = 19.861109438 Simplifying x + -29.41176471 = 19.861109438 Reorder the terms: -29.41176471 + x = 19.861109438 Solving -29.41176471 + x = 19.861109438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '29.41176471' to each side of the equation. -29.41176471 + 29.41176471 + x = 19.861109438 + 29.41176471 Combine like terms: -29.41176471 + 29.41176471 = 0.00000000 0.00000000 + x = 19.861109438 + 29.41176471 x = 19.861109438 + 29.41176471 Combine like terms: 19.861109438 + 29.41176471 = 49.272874148 x = 49.272874148 Simplifying x = 49.272874148Subproblem 2
x + -29.41176471 = -19.861109438 Simplifying x + -29.41176471 = -19.861109438 Reorder the terms: -29.41176471 + x = -19.861109438 Solving -29.41176471 + x = -19.861109438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '29.41176471' to each side of the equation. -29.41176471 + 29.41176471 + x = -19.861109438 + 29.41176471 Combine like terms: -29.41176471 + 29.41176471 = 0.00000000 0.00000000 + x = -19.861109438 + 29.41176471 x = -19.861109438 + 29.41176471 Combine like terms: -19.861109438 + 29.41176471 = 9.550655272 x = 9.550655272 Simplifying x = 9.550655272Solution
The solution to the problem is based on the solutions from the subproblems. x = {49.272874148, 9.550655272}
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