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Simplifying 6x2 = 64x + -96 Reorder the terms: 6x2 = -96 + 64x Solving 6x2 = -96 + 64x Solving for variable 'x'. Reorder the terms: 96 + -64x + 6x2 = -96 + 64x + 96 + -64x Reorder the terms: 96 + -64x + 6x2 = -96 + 96 + 64x + -64x Combine like terms: -96 + 96 = 0 96 + -64x + 6x2 = 0 + 64x + -64x 96 + -64x + 6x2 = 64x + -64x Combine like terms: 64x + -64x = 0 96 + -64x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(48 + -32x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(48 + -32x + 3x2)' equal to zero and attempt to solve: Simplifying 48 + -32x + 3x2 = 0 Solving 48 + -32x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 16 + -10.66666667x + x2 = 0 Move the constant term to the right: Add '-16' to each side of the equation. 16 + -10.66666667x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + -10.66666667x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -10.66666667x + x2 = 0 + -16 -10.66666667x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 -10.66666667x + x2 = -16 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 = -16 + 28.44444446 Reorder the terms: 28.44444446 + -10.66666667x + x2 = -16 + 28.44444446 Combine like terms: -16 + 28.44444446 = 12.44444446 28.44444446 + -10.66666667x + x2 = 12.44444446 Factor a perfect square on the left side: (x + -5.333333335)(x + -5.333333335) = 12.44444446 Calculate the square root of the right side: 3.527668417 Break this problem into two subproblems by setting (x + -5.333333335) equal to 3.527668417 and -3.527668417.Subproblem 1
x + -5.333333335 = 3.527668417 Simplifying x + -5.333333335 = 3.527668417 Reorder the terms: -5.333333335 + x = 3.527668417 Solving -5.333333335 + x = 3.527668417 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 = 3.527668417 + 5.333333335 Combine like terms: -5.333333335 + 5.333333335 = 0.000000000 0.000000000 + x = 3.527668417 + 5.333333335 x = 3.527668417 + 5.333333335 Combine like terms: 3.527668417 + 5.333333335 = 8.861001752 x = 8.861001752 Simplifying x = 8.861001752Subproblem 2
x + -5.333333335 = -3.527668417 Simplifying x + -5.333333335 = -3.527668417 Reorder the terms: -5.333333335 + x = -3.527668417 Solving -5.333333335 + x = -3.527668417 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 = -3.527668417 + 5.333333335 Combine like terms: -5.333333335 + 5.333333335 = 0.000000000 0.000000000 + x = -3.527668417 + 5.333333335 x = -3.527668417 + 5.333333335 Combine like terms: -3.527668417 + 5.333333335 = 1.805664918 x = 1.805664918 Simplifying x = 1.805664918Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.861001752, 1.805664918}Solution
x = {8.861001752, 1.805664918}
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