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Simplifying 2x2 + 40x = 5985 Reorder the terms: 40x + 2x2 = 5985 Solving 40x + 2x2 = 5985 Solving for variable 'x'. Reorder the terms: -5985 + 40x + 2x2 = 5985 + -5985 Combine like terms: 5985 + -5985 = 0 -5985 + 40x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2992.5 + 20x + x2 = 0 Move the constant term to the right: Add '2992.5' to each side of the equation. -2992.5 + 20x + 2992.5 + x2 = 0 + 2992.5 Reorder the terms: -2992.5 + 2992.5 + 20x + x2 = 0 + 2992.5 Combine like terms: -2992.5 + 2992.5 = 0.0 0.0 + 20x + x2 = 0 + 2992.5 20x + x2 = 0 + 2992.5 Combine like terms: 0 + 2992.5 = 2992.5 20x + x2 = 2992.5 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 2992.5 + 100 Reorder the terms: 100 + 20x + x2 = 2992.5 + 100 Combine like terms: 2992.5 + 100 = 3092.5 100 + 20x + x2 = 3092.5 Factor a perfect square on the left side: (x + 10)(x + 10) = 3092.5 Calculate the square root of the right side: 55.610250854 Break this problem into two subproblems by setting (x + 10) equal to 55.610250854 and -55.610250854.Subproblem 1
x + 10 = 55.610250854 Simplifying x + 10 = 55.610250854 Reorder the terms: 10 + x = 55.610250854 Solving 10 + x = 55.610250854 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 55.610250854 + -10 Combine like terms: 10 + -10 = 0 0 + x = 55.610250854 + -10 x = 55.610250854 + -10 Combine like terms: 55.610250854 + -10 = 45.610250854 x = 45.610250854 Simplifying x = 45.610250854Subproblem 2
x + 10 = -55.610250854 Simplifying x + 10 = -55.610250854 Reorder the terms: 10 + x = -55.610250854 Solving 10 + x = -55.610250854 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -55.610250854 + -10 Combine like terms: 10 + -10 = 0 0 + x = -55.610250854 + -10 x = -55.610250854 + -10 Combine like terms: -55.610250854 + -10 = -65.610250854 x = -65.610250854 Simplifying x = -65.610250854Solution
The solution to the problem is based on the solutions from the subproblems. x = {45.610250854, -65.610250854}
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