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Simplifying x2 + 40x + 384 = 80 Reorder the terms: 384 + 40x + x2 = 80 Solving 384 + 40x + x2 = 80 Solving for variable 'x'. Reorder the terms: 384 + -80 + 40x + x2 = 80 + -80 Combine like terms: 384 + -80 = 304 304 + 40x + x2 = 80 + -80 Combine like terms: 80 + -80 = 0 304 + 40x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-304' to each side of the equation. 304 + 40x + -304 + x2 = 0 + -304 Reorder the terms: 304 + -304 + 40x + x2 = 0 + -304 Combine like terms: 304 + -304 = 0 0 + 40x + x2 = 0 + -304 40x + x2 = 0 + -304 Combine like terms: 0 + -304 = -304 40x + x2 = -304 The x term is 40x. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40x + 400 + x2 = -304 + 400 Reorder the terms: 400 + 40x + x2 = -304 + 400 Combine like terms: -304 + 400 = 96 400 + 40x + x2 = 96 Factor a perfect square on the left side: (x + 20)(x + 20) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (x + 20) equal to 9.797958971 and -9.797958971.Subproblem 1
x + 20 = 9.797958971 Simplifying x + 20 = 9.797958971 Reorder the terms: 20 + x = 9.797958971 Solving 20 + x = 9.797958971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 9.797958971 + -20 Combine like terms: 20 + -20 = 0 0 + x = 9.797958971 + -20 x = 9.797958971 + -20 Combine like terms: 9.797958971 + -20 = -10.202041029 x = -10.202041029 Simplifying x = -10.202041029Subproblem 2
x + 20 = -9.797958971 Simplifying x + 20 = -9.797958971 Reorder the terms: 20 + x = -9.797958971 Solving 20 + x = -9.797958971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = -9.797958971 + -20 Combine like terms: 20 + -20 = 0 0 + x = -9.797958971 + -20 x = -9.797958971 + -20 Combine like terms: -9.797958971 + -20 = -29.797958971 x = -29.797958971 Simplifying x = -29.797958971Solution
The solution to the problem is based on the solutions from the subproblems. x = {-10.202041029, -29.797958971}
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