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Simplifying 6x2 + -64x + 60 = 0 Reorder the terms: 60 + -64x + 6x2 = 0 Solving 60 + -64x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(30 + -32x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(30 + -32x + 3x2)' equal to zero and attempt to solve: Simplifying 30 + -32x + 3x2 = 0 Solving 30 + -32x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 10 + -10.66666667x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -10.66666667x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -10.66666667x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -10.66666667x + x2 = 0 + -10 -10.66666667x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -10.66666667x + x2 = -10 The x term is -10.66666667x. Take half its coefficient (-5.333333335). Square it (28.44444446) and add it to both sides. Add '28.44444446' to each side of the equation. -10.66666667x + 28.44444446 + x2 = -10 + 28.44444446 Reorder the terms: 28.44444446 + -10.66666667x + x2 = -10 + 28.44444446 Combine like terms: -10 + 28.44444446 = 18.44444446 28.44444446 + -10.66666667x + x2 = 18.44444446 Factor a perfect square on the left side: (x + -5.333333335)(x + -5.333333335) = 18.44444446 Calculate the square root of the right side: 4.294699577 Break this problem into two subproblems by setting (x + -5.333333335) equal to 4.294699577 and -4.294699577.Subproblem 1
x + -5.333333335 = 4.294699577 Simplifying x + -5.333333335 = 4.294699577 Reorder the terms: -5.333333335 + x = 4.294699577 Solving -5.333333335 + x = 4.294699577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.333333335' to each side of the equation. -5.333333335 + 5.333333335 + x = 4.294699577 + 5.333333335 Combine like terms: -5.333333335 + 5.333333335 = 0.000000000 0.000000000 + x = 4.294699577 + 5.333333335 x = 4.294699577 + 5.333333335 Combine like terms: 4.294699577 + 5.333333335 = 9.628032912 x = 9.628032912 Simplifying x = 9.628032912Subproblem 2
x + -5.333333335 = -4.294699577 Simplifying x + -5.333333335 = -4.294699577 Reorder the terms: -5.333333335 + x = -4.294699577 Solving -5.333333335 + x = -4.294699577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.333333335' to each side of the equation. -5.333333335 + 5.333333335 + x = -4.294699577 + 5.333333335 Combine like terms: -5.333333335 + 5.333333335 = 0.000000000 0.000000000 + x = -4.294699577 + 5.333333335 x = -4.294699577 + 5.333333335 Combine like terms: -4.294699577 + 5.333333335 = 1.038633758 x = 1.038633758 Simplifying x = 1.038633758Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.628032912, 1.038633758}Solution
x = {9.628032912, 1.038633758}
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