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Simplifying 6x2 + 224x + 480 = 0 Reorder the terms: 480 + 224x + 6x2 = 0 Solving 480 + 224x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(240 + 112x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(240 + 112x + 3x2)' equal to zero and attempt to solve: Simplifying 240 + 112x + 3x2 = 0 Solving 240 + 112x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 80 + 37.33333333x + x2 = 0 Move the constant term to the right: Add '-80' to each side of the equation. 80 + 37.33333333x + -80 + x2 = 0 + -80 Reorder the terms: 80 + -80 + 37.33333333x + x2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + 37.33333333x + x2 = 0 + -80 37.33333333x + x2 = 0 + -80 Combine like terms: 0 + -80 = -80 37.33333333x + x2 = -80 The x term is 37.33333333x. Take half its coefficient (18.66666667). Square it (348.4444446) and add it to both sides. Add '348.4444446' to each side of the equation. 37.33333333x + 348.4444446 + x2 = -80 + 348.4444446 Reorder the terms: 348.4444446 + 37.33333333x + x2 = -80 + 348.4444446 Combine like terms: -80 + 348.4444446 = 268.4444446 348.4444446 + 37.33333333x + x2 = 268.4444446 Factor a perfect square on the left side: (x + 18.66666667)(x + 18.66666667) = 268.4444446 Calculate the square root of the right side: 16.384274308 Break this problem into two subproblems by setting (x + 18.66666667) equal to 16.384274308 and -16.384274308.Subproblem 1
x + 18.66666667 = 16.384274308 Simplifying x + 18.66666667 = 16.384274308 Reorder the terms: 18.66666667 + x = 16.384274308 Solving 18.66666667 + x = 16.384274308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.66666667' to each side of the equation. 18.66666667 + -18.66666667 + x = 16.384274308 + -18.66666667 Combine like terms: 18.66666667 + -18.66666667 = 0.00000000 0.00000000 + x = 16.384274308 + -18.66666667 x = 16.384274308 + -18.66666667 Combine like terms: 16.384274308 + -18.66666667 = -2.282392362 x = -2.282392362 Simplifying x = -2.282392362Subproblem 2
x + 18.66666667 = -16.384274308 Simplifying x + 18.66666667 = -16.384274308 Reorder the terms: 18.66666667 + x = -16.384274308 Solving 18.66666667 + x = -16.384274308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.66666667' to each side of the equation. 18.66666667 + -18.66666667 + x = -16.384274308 + -18.66666667 Combine like terms: 18.66666667 + -18.66666667 = 0.00000000 0.00000000 + x = -16.384274308 + -18.66666667 x = -16.384274308 + -18.66666667 Combine like terms: -16.384274308 + -18.66666667 = -35.050940978 x = -35.050940978 Simplifying x = -35.050940978Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.282392362, -35.050940978}Solution
x = {-2.282392362, -35.050940978}
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