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Simplifying 7x2 + -308.7x + 1577.66 = 0 Reorder the terms: 1577.66 + -308.7x + 7x2 = 0 Solving 1577.66 + -308.7x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 225.38 + -44.1x + x2 = 0 Move the constant term to the right: Add '-225.38' to each side of the equation. 225.38 + -44.1x + -225.38 + x2 = 0 + -225.38 Reorder the terms: 225.38 + -225.38 + -44.1x + x2 = 0 + -225.38 Combine like terms: 225.38 + -225.38 = 0.00 0.00 + -44.1x + x2 = 0 + -225.38 -44.1x + x2 = 0 + -225.38 Combine like terms: 0 + -225.38 = -225.38 -44.1x + x2 = -225.38 The x term is -44.1x. Take half its coefficient (-22.05). Square it (486.2025) and add it to both sides. Add '486.2025' to each side of the equation. -44.1x + 486.2025 + x2 = -225.38 + 486.2025 Reorder the terms: 486.2025 + -44.1x + x2 = -225.38 + 486.2025 Combine like terms: -225.38 + 486.2025 = 260.8225 486.2025 + -44.1x + x2 = 260.8225 Factor a perfect square on the left side: (x + -22.05)(x + -22.05) = 260.8225 Calculate the square root of the right side: 16.15 Break this problem into two subproblems by setting (x + -22.05) equal to 16.15 and -16.15.Subproblem 1
x + -22.05 = 16.15 Simplifying x + -22.05 = 16.15 Reorder the terms: -22.05 + x = 16.15 Solving -22.05 + x = 16.15 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.05' to each side of the equation. -22.05 + 22.05 + x = 16.15 + 22.05 Combine like terms: -22.05 + 22.05 = 0.00 0.00 + x = 16.15 + 22.05 x = 16.15 + 22.05 Combine like terms: 16.15 + 22.05 = 38.2 x = 38.2 Simplifying x = 38.2Subproblem 2
x + -22.05 = -16.15 Simplifying x + -22.05 = -16.15 Reorder the terms: -22.05 + x = -16.15 Solving -22.05 + x = -16.15 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.05' to each side of the equation. -22.05 + 22.05 + x = -16.15 + 22.05 Combine like terms: -22.05 + 22.05 = 0.00 0.00 + x = -16.15 + 22.05 x = -16.15 + 22.05 Combine like terms: -16.15 + 22.05 = 5.9 x = 5.9 Simplifying x = 5.9Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.2, 5.9}
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