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Simplifying 22x2 + 40x = 80 Reorder the terms: 40x + 22x2 = 80 Solving 40x + 22x2 = 80 Solving for variable 'x'. Reorder the terms: -80 + 40x + 22x2 = 80 + -80 Combine like terms: 80 + -80 = 0 -80 + 40x + 22x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-40 + 20x + 11x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-40 + 20x + 11x2)' equal to zero and attempt to solve: Simplifying -40 + 20x + 11x2 = 0 Solving -40 + 20x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -3.636363636 + 1.818181818x + x2 = 0 Move the constant term to the right: Add '3.636363636' to each side of the equation. -3.636363636 + 1.818181818x + 3.636363636 + x2 = 0 + 3.636363636 Reorder the terms: -3.636363636 + 3.636363636 + 1.818181818x + x2 = 0 + 3.636363636 Combine like terms: -3.636363636 + 3.636363636 = 0.000000000 0.000000000 + 1.818181818x + x2 = 0 + 3.636363636 1.818181818x + x2 = 0 + 3.636363636 Combine like terms: 0 + 3.636363636 = 3.636363636 1.818181818x + x2 = 3.636363636 The x term is 1.818181818x. Take half its coefficient (0.909090909). Square it (0.8264462808) and add it to both sides. Add '0.8264462808' to each side of the equation. 1.818181818x + 0.8264462808 + x2 = 3.636363636 + 0.8264462808 Reorder the terms: 0.8264462808 + 1.818181818x + x2 = 3.636363636 + 0.8264462808 Combine like terms: 3.636363636 + 0.8264462808 = 4.4628099168 0.8264462808 + 1.818181818x + x2 = 4.4628099168 Factor a perfect square on the left side: (x + 0.909090909)(x + 0.909090909) = 4.4628099168 Calculate the square root of the right side: 2.112536371 Break this problem into two subproblems by setting (x + 0.909090909) equal to 2.112536371 and -2.112536371.Subproblem 1
x + 0.909090909 = 2.112536371 Simplifying x + 0.909090909 = 2.112536371 Reorder the terms: 0.909090909 + x = 2.112536371 Solving 0.909090909 + x = 2.112536371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.909090909' to each side of the equation. 0.909090909 + -0.909090909 + x = 2.112536371 + -0.909090909 Combine like terms: 0.909090909 + -0.909090909 = 0.000000000 0.000000000 + x = 2.112536371 + -0.909090909 x = 2.112536371 + -0.909090909 Combine like terms: 2.112536371 + -0.909090909 = 1.203445462 x = 1.203445462 Simplifying x = 1.203445462Subproblem 2
x + 0.909090909 = -2.112536371 Simplifying x + 0.909090909 = -2.112536371 Reorder the terms: 0.909090909 + x = -2.112536371 Solving 0.909090909 + x = -2.112536371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.909090909' to each side of the equation. 0.909090909 + -0.909090909 + x = -2.112536371 + -0.909090909 Combine like terms: 0.909090909 + -0.909090909 = 0.000000000 0.000000000 + x = -2.112536371 + -0.909090909 x = -2.112536371 + -0.909090909 Combine like terms: -2.112536371 + -0.909090909 = -3.02162728 x = -3.02162728 Simplifying x = -3.02162728Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.203445462, -3.02162728}Solution
x = {1.203445462, -3.02162728}
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