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Simplifying 12x2 = 48x + -32 Reorder the terms: 12x2 = -32 + 48x Solving 12x2 = -32 + 48x Solving for variable 'x'. Reorder the terms: 32 + -48x + 12x2 = -32 + 48x + 32 + -48x Reorder the terms: 32 + -48x + 12x2 = -32 + 32 + 48x + -48x Combine like terms: -32 + 32 = 0 32 + -48x + 12x2 = 0 + 48x + -48x 32 + -48x + 12x2 = 48x + -48x Combine like terms: 48x + -48x = 0 32 + -48x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(8 + -12x + 3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(8 + -12x + 3x2)' equal to zero and attempt to solve: Simplifying 8 + -12x + 3x2 = 0 Solving 8 + -12x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.666666667 + -4x + x2 = 0 Move the constant term to the right: Add '-2.666666667' to each side of the equation. 2.666666667 + -4x + -2.666666667 + x2 = 0 + -2.666666667 Reorder the terms: 2.666666667 + -2.666666667 + -4x + x2 = 0 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + -4x + x2 = 0 + -2.666666667 -4x + x2 = 0 + -2.666666667 Combine like terms: 0 + -2.666666667 = -2.666666667 -4x + x2 = -2.666666667 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -2.666666667 + 4 Reorder the terms: 4 + -4x + x2 = -2.666666667 + 4 Combine like terms: -2.666666667 + 4 = 1.333333333 4 + -4x + x2 = 1.333333333 Factor a perfect square on the left side: (x + -2)(x + -2) = 1.333333333 Calculate the square root of the right side: 1.154700538 Break this problem into two subproblems by setting (x + -2) equal to 1.154700538 and -1.154700538.Subproblem 1
x + -2 = 1.154700538 Simplifying x + -2 = 1.154700538 Reorder the terms: -2 + x = 1.154700538 Solving -2 + x = 1.154700538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.154700538 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.154700538 + 2 x = 1.154700538 + 2 Combine like terms: 1.154700538 + 2 = 3.154700538 x = 3.154700538 Simplifying x = 3.154700538Subproblem 2
x + -2 = -1.154700538 Simplifying x + -2 = -1.154700538 Reorder the terms: -2 + x = -1.154700538 Solving -2 + x = -1.154700538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.154700538 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.154700538 + 2 x = -1.154700538 + 2 Combine like terms: -1.154700538 + 2 = 0.845299462 x = 0.845299462 Simplifying x = 0.845299462Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.154700538, 0.845299462}Solution
x = {3.154700538, 0.845299462}
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