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Simplifying 6x2 + 10x + -64 = 0 Reorder the terms: -64 + 10x + 6x2 = 0 Solving -64 + 10x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-32 + 5x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-32 + 5x + 3x2)' equal to zero and attempt to solve: Simplifying -32 + 5x + 3x2 = 0 Solving -32 + 5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -10.66666667 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '10.66666667' to each side of the equation. -10.66666667 + 1.666666667x + 10.66666667 + x2 = 0 + 10.66666667 Reorder the terms: -10.66666667 + 10.66666667 + 1.666666667x + x2 = 0 + 10.66666667 Combine like terms: -10.66666667 + 10.66666667 = 0.00000000 0.00000000 + 1.666666667x + x2 = 0 + 10.66666667 1.666666667x + x2 = 0 + 10.66666667 Combine like terms: 0 + 10.66666667 = 10.66666667 1.666666667x + x2 = 10.66666667 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 10.66666667 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 10.66666667 + 0.6944444447 Combine like terms: 10.66666667 + 0.6944444447 = 11.3611111147 0.6944444447 + 1.666666667x + x2 = 11.3611111147 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 11.3611111147 Calculate the square root of the right side: 3.370624737 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 3.370624737 and -3.370624737.Subproblem 1
x + 0.8333333335 = 3.370624737 Simplifying x + 0.8333333335 = 3.370624737 Reorder the terms: 0.8333333335 + x = 3.370624737 Solving 0.8333333335 + x = 3.370624737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 3.370624737 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 3.370624737 + -0.8333333335 x = 3.370624737 + -0.8333333335 Combine like terms: 3.370624737 + -0.8333333335 = 2.5372914035 x = 2.5372914035 Simplifying x = 2.5372914035Subproblem 2
x + 0.8333333335 = -3.370624737 Simplifying x + 0.8333333335 = -3.370624737 Reorder the terms: 0.8333333335 + x = -3.370624737 Solving 0.8333333335 + x = -3.370624737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -3.370624737 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -3.370624737 + -0.8333333335 x = -3.370624737 + -0.8333333335 Combine like terms: -3.370624737 + -0.8333333335 = -4.2039580705 x = -4.2039580705 Simplifying x = -4.2039580705Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.5372914035, -4.2039580705}Solution
x = {2.5372914035, -4.2039580705}
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