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Simplifying 6x2 = 6x + 16 Reorder the terms: 6x2 = 16 + 6x Solving 6x2 = 16 + 6x Solving for variable 'x'. Reorder the terms: -16 + -6x + 6x2 = 16 + 6x + -16 + -6x Reorder the terms: -16 + -6x + 6x2 = 16 + -16 + 6x + -6x Combine like terms: 16 + -16 = 0 -16 + -6x + 6x2 = 0 + 6x + -6x -16 + -6x + 6x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -16 + -6x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + -3x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + -3x + 3x2)' equal to zero and attempt to solve: Simplifying -8 + -3x + 3x2 = 0 Solving -8 + -3x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.666666667 + -1x + x2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + -1x + 2.666666667 + x2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + -1x + x2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + -1x + x2 = 0 + 2.666666667 -1x + x2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 -1x + x2 = 2.666666667 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 2.666666667 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 2.666666667 + 0.25 Combine like terms: 2.666666667 + 0.25 = 2.916666667 0.25 + -1x + x2 = 2.916666667 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 2.916666667 Calculate the square root of the right side: 1.707825128 Break this problem into two subproblems by setting (x + -0.5) equal to 1.707825128 and -1.707825128.Subproblem 1
x + -0.5 = 1.707825128 Simplifying x + -0.5 = 1.707825128 Reorder the terms: -0.5 + x = 1.707825128 Solving -0.5 + x = 1.707825128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.707825128 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.707825128 + 0.5 x = 1.707825128 + 0.5 Combine like terms: 1.707825128 + 0.5 = 2.207825128 x = 2.207825128 Simplifying x = 2.207825128Subproblem 2
x + -0.5 = -1.707825128 Simplifying x + -0.5 = -1.707825128 Reorder the terms: -0.5 + x = -1.707825128 Solving -0.5 + x = -1.707825128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.707825128 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.707825128 + 0.5 x = -1.707825128 + 0.5 Combine like terms: -1.707825128 + 0.5 = -1.207825128 x = -1.207825128 Simplifying x = -1.207825128Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.207825128, -1.207825128}Solution
x = {2.207825128, -1.207825128}
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