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Simplifying 4x2 + 22x + -240 = 0 Reorder the terms: -240 + 22x + 4x2 = 0 Solving -240 + 22x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-120 + 11x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-120 + 11x + 2x2)' equal to zero and attempt to solve: Simplifying -120 + 11x + 2x2 = 0 Solving -120 + 11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -60 + 5.5x + x2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + 5.5x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + 5.5x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 5.5x + x2 = 0 + 60 5.5x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 5.5x + x2 = 60 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = 60 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = 60 + 7.5625 Combine like terms: 60 + 7.5625 = 67.5625 7.5625 + 5.5x + x2 = 67.5625 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 67.5625 Calculate the square root of the right side: 8.219641111 Break this problem into two subproblems by setting (x + 2.75) equal to 8.219641111 and -8.219641111.Subproblem 1
x + 2.75 = 8.219641111 Simplifying x + 2.75 = 8.219641111 Reorder the terms: 2.75 + x = 8.219641111 Solving 2.75 + x = 8.219641111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 8.219641111 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 8.219641111 + -2.75 x = 8.219641111 + -2.75 Combine like terms: 8.219641111 + -2.75 = 5.469641111 x = 5.469641111 Simplifying x = 5.469641111Subproblem 2
x + 2.75 = -8.219641111 Simplifying x + 2.75 = -8.219641111 Reorder the terms: 2.75 + x = -8.219641111 Solving 2.75 + x = -8.219641111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -8.219641111 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -8.219641111 + -2.75 x = -8.219641111 + -2.75 Combine like terms: -8.219641111 + -2.75 = -10.969641111 x = -10.969641111 Simplifying x = -10.969641111Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.469641111, -10.969641111}Solution
x = {5.469641111, -10.969641111}
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