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Simplifying 6x2 = 12x + 28 Reorder the terms: 6x2 = 28 + 12x Solving 6x2 = 28 + 12x Solving for variable 'x'. Reorder the terms: -28 + -12x + 6x2 = 28 + 12x + -28 + -12x Reorder the terms: -28 + -12x + 6x2 = 28 + -28 + 12x + -12x Combine like terms: 28 + -28 = 0 -28 + -12x + 6x2 = 0 + 12x + -12x -28 + -12x + 6x2 = 12x + -12x Combine like terms: 12x + -12x = 0 -28 + -12x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-14 + -6x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-14 + -6x + 3x2)' equal to zero and attempt to solve: Simplifying -14 + -6x + 3x2 = 0 Solving -14 + -6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -4.666666667 + -2x + x2 = 0 Move the constant term to the right: Add '4.666666667' to each side of the equation. -4.666666667 + -2x + 4.666666667 + x2 = 0 + 4.666666667 Reorder the terms: -4.666666667 + 4.666666667 + -2x + x2 = 0 + 4.666666667 Combine like terms: -4.666666667 + 4.666666667 = 0.000000000 0.000000000 + -2x + x2 = 0 + 4.666666667 -2x + x2 = 0 + 4.666666667 Combine like terms: 0 + 4.666666667 = 4.666666667 -2x + x2 = 4.666666667 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 4.666666667 + 1 Reorder the terms: 1 + -2x + x2 = 4.666666667 + 1 Combine like terms: 4.666666667 + 1 = 5.666666667 1 + -2x + x2 = 5.666666667 Factor a perfect square on the left side: (x + -1)(x + -1) = 5.666666667 Calculate the square root of the right side: 2.380476143 Break this problem into two subproblems by setting (x + -1) equal to 2.380476143 and -2.380476143.Subproblem 1
x + -1 = 2.380476143 Simplifying x + -1 = 2.380476143 Reorder the terms: -1 + x = 2.380476143 Solving -1 + x = 2.380476143 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.380476143 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.380476143 + 1 x = 2.380476143 + 1 Combine like terms: 2.380476143 + 1 = 3.380476143 x = 3.380476143 Simplifying x = 3.380476143Subproblem 2
x + -1 = -2.380476143 Simplifying x + -1 = -2.380476143 Reorder the terms: -1 + x = -2.380476143 Solving -1 + x = -2.380476143 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.380476143 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.380476143 + 1 x = -2.380476143 + 1 Combine like terms: -2.380476143 + 1 = -1.380476143 x = -1.380476143 Simplifying x = -1.380476143Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.380476143, -1.380476143}Solution
x = {3.380476143, -1.380476143}
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