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Simplifying -0.04x2 + 2.1x + 6.1 = 0 Reorder the terms: 6.1 + 2.1x + -0.04x2 = 0 Solving 6.1 + 2.1x + -0.04x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.04 the coefficient of the squared term: Divide each side by '-0.04'. -152.5 + -52.5x + x2 = 0 Move the constant term to the right: Add '152.5' to each side of the equation. -152.5 + -52.5x + 152.5 + x2 = 0 + 152.5 Reorder the terms: -152.5 + 152.5 + -52.5x + x2 = 0 + 152.5 Combine like terms: -152.5 + 152.5 = 0.0 0.0 + -52.5x + x2 = 0 + 152.5 -52.5x + x2 = 0 + 152.5 Combine like terms: 0 + 152.5 = 152.5 -52.5x + x2 = 152.5 The x term is -52.5x. Take half its coefficient (-26.25). Square it (689.0625) and add it to both sides. Add '689.0625' to each side of the equation. -52.5x + 689.0625 + x2 = 152.5 + 689.0625 Reorder the terms: 689.0625 + -52.5x + x2 = 152.5 + 689.0625 Combine like terms: 152.5 + 689.0625 = 841.5625 689.0625 + -52.5x + x2 = 841.5625 Factor a perfect square on the left side: (x + -26.25)(x + -26.25) = 841.5625 Calculate the square root of the right side: 29.009696655 Break this problem into two subproblems by setting (x + -26.25) equal to 29.009696655 and -29.009696655.Subproblem 1
x + -26.25 = 29.009696655 Simplifying x + -26.25 = 29.009696655 Reorder the terms: -26.25 + x = 29.009696655 Solving -26.25 + x = 29.009696655 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26.25' to each side of the equation. -26.25 + 26.25 + x = 29.009696655 + 26.25 Combine like terms: -26.25 + 26.25 = 0.00 0.00 + x = 29.009696655 + 26.25 x = 29.009696655 + 26.25 Combine like terms: 29.009696655 + 26.25 = 55.259696655 x = 55.259696655 Simplifying x = 55.259696655Subproblem 2
x + -26.25 = -29.009696655 Simplifying x + -26.25 = -29.009696655 Reorder the terms: -26.25 + x = -29.009696655 Solving -26.25 + x = -29.009696655 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26.25' to each side of the equation. -26.25 + 26.25 + x = -29.009696655 + 26.25 Combine like terms: -26.25 + 26.25 = 0.00 0.00 + x = -29.009696655 + 26.25 x = -29.009696655 + 26.25 Combine like terms: -29.009696655 + 26.25 = -2.759696655 x = -2.759696655 Simplifying x = -2.759696655Solution
The solution to the problem is based on the solutions from the subproblems. x = {55.259696655, -2.759696655}
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