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Simplifying 6x2 + 4x + -480 = 0 Reorder the terms: -480 + 4x + 6x2 = 0 Solving -480 + 4x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-240 + 2x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-240 + 2x + 3x2)' equal to zero and attempt to solve: Simplifying -240 + 2x + 3x2 = 0 Solving -240 + 2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -80 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '80' to each side of the equation. -80 + 0.6666666667x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + 0.6666666667x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + 0.6666666667x + x2 = 0 + 80 0.6666666667x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 0.6666666667x + x2 = 80 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 80 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 80 + 0.1111111112 Combine like terms: 80 + 0.1111111112 = 80.1111111112 0.1111111112 + 0.6666666667x + x2 = 80.1111111112 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 80.1111111112 Calculate the square root of the right side: 8.950481055 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 8.950481055 and -8.950481055.Subproblem 1
x + 0.3333333334 = 8.950481055 Simplifying x + 0.3333333334 = 8.950481055 Reorder the terms: 0.3333333334 + x = 8.950481055 Solving 0.3333333334 + x = 8.950481055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 8.950481055 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 8.950481055 + -0.3333333334 x = 8.950481055 + -0.3333333334 Combine like terms: 8.950481055 + -0.3333333334 = 8.6171477216 x = 8.6171477216 Simplifying x = 8.6171477216Subproblem 2
x + 0.3333333334 = -8.950481055 Simplifying x + 0.3333333334 = -8.950481055 Reorder the terms: 0.3333333334 + x = -8.950481055 Solving 0.3333333334 + x = -8.950481055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -8.950481055 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -8.950481055 + -0.3333333334 x = -8.950481055 + -0.3333333334 Combine like terms: -8.950481055 + -0.3333333334 = -9.2838143884 x = -9.2838143884 Simplifying x = -9.2838143884Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.6171477216, -9.2838143884}Solution
x = {8.6171477216, -9.2838143884}
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