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Simplifying x2 + 40x + -80 = 0 Reorder the terms: -80 + 40x + x2 = 0 Solving -80 + 40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '80' to each side of the equation. -80 + 40x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + 40x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + 40x + x2 = 0 + 80 40x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 40x + x2 = 80 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 = 80 + 400 Reorder the terms: 400 + 40x + x2 = 80 + 400 Combine like terms: 80 + 400 = 480 400 + 40x + x2 = 480 Factor a perfect square on the left side: (x + 20)(x + 20) = 480 Calculate the square root of the right side: 21.9089023 Break this problem into two subproblems by setting (x + 20) equal to 21.9089023 and -21.9089023.Subproblem 1
x + 20 = 21.9089023 Simplifying x + 20 = 21.9089023 Reorder the terms: 20 + x = 21.9089023 Solving 20 + x = 21.9089023 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 = 21.9089023 + -20 Combine like terms: 20 + -20 = 0 0 + x = 21.9089023 + -20 x = 21.9089023 + -20 Combine like terms: 21.9089023 + -20 = 1.9089023 x = 1.9089023 Simplifying x = 1.9089023Subproblem 2
x + 20 = -21.9089023 Simplifying x + 20 = -21.9089023 Reorder the terms: 20 + x = -21.9089023 Solving 20 + x = -21.9089023 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 = -21.9089023 + -20 Combine like terms: 20 + -20 = 0 0 + x = -21.9089023 + -20 x = -21.9089023 + -20 Combine like terms: -21.9089023 + -20 = -41.9089023 x = -41.9089023 Simplifying x = -41.9089023Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9089023, -41.9089023}
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