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Simplifying 12x(x + -2) + -6 = 3x + 6 Reorder the terms: 12x(-2 + x) + -6 = 3x + 6 (-2 * 12x + x * 12x) + -6 = 3x + 6 (-24x + 12x2) + -6 = 3x + 6 Reorder the terms: -6 + -24x + 12x2 = 3x + 6 Reorder the terms: -6 + -24x + 12x2 = 6 + 3x Solving -6 + -24x + 12x2 = 6 + 3x Solving for variable 'x'. Reorder the terms: -6 + -6 + -24x + -3x + 12x2 = 6 + 3x + -6 + -3x Combine like terms: -6 + -6 = -12 -12 + -24x + -3x + 12x2 = 6 + 3x + -6 + -3x Combine like terms: -24x + -3x = -27x -12 + -27x + 12x2 = 6 + 3x + -6 + -3x Reorder the terms: -12 + -27x + 12x2 = 6 + -6 + 3x + -3x Combine like terms: 6 + -6 = 0 -12 + -27x + 12x2 = 0 + 3x + -3x -12 + -27x + 12x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -12 + -27x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + -9x + 4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + -9x + 4x2)' equal to zero and attempt to solve: Simplifying -4 + -9x + 4x2 = 0 Solving -4 + -9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1 + -2.25x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -2.25x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -2.25x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2.25x + x2 = 0 + 1 -2.25x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -2.25x + x2 = 1 The x term is -2.25x. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25x + 1.265625 + x2 = 1 + 1.265625 Reorder the terms: 1.265625 + -2.25x + x2 = 1 + 1.265625 Combine like terms: 1 + 1.265625 = 2.265625 1.265625 + -2.25x + x2 = 2.265625 Factor a perfect square on the left side: (x + -1.125)(x + -1.125) = 2.265625 Calculate the square root of the right side: 1.505199322 Break this problem into two subproblems by setting (x + -1.125) equal to 1.505199322 and -1.505199322.Subproblem 1
x + -1.125 = 1.505199322 Simplifying x + -1.125 = 1.505199322 Reorder the terms: -1.125 + x = 1.505199322 Solving -1.125 + x = 1.505199322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = 1.505199322 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 1.505199322 + 1.125 x = 1.505199322 + 1.125 Combine like terms: 1.505199322 + 1.125 = 2.630199322 x = 2.630199322 Simplifying x = 2.630199322Subproblem 2
x + -1.125 = -1.505199322 Simplifying x + -1.125 = -1.505199322 Reorder the terms: -1.125 + x = -1.505199322 Solving -1.125 + x = -1.505199322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = -1.505199322 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -1.505199322 + 1.125 x = -1.505199322 + 1.125 Combine like terms: -1.505199322 + 1.125 = -0.380199322 x = -0.380199322 Simplifying x = -0.380199322Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.630199322, -0.380199322}Solution
x = {2.630199322, -0.380199322}
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