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Simplifying 6x(2x + -1) + -12 = 3(7x + 4) Reorder the terms: 6x(-1 + 2x) + -12 = 3(7x + 4) (-1 * 6x + 2x * 6x) + -12 = 3(7x + 4) (-6x + 12x2) + -12 = 3(7x + 4) Reorder the terms: -12 + -6x + 12x2 = 3(7x + 4) Reorder the terms: -12 + -6x + 12x2 = 3(4 + 7x) -12 + -6x + 12x2 = (4 * 3 + 7x * 3) -12 + -6x + 12x2 = (12 + 21x) Solving -12 + -6x + 12x2 = 12 + 21x Solving for variable 'x'. Reorder the terms: -12 + -12 + -6x + -21x + 12x2 = 12 + 21x + -12 + -21x Combine like terms: -12 + -12 = -24 -24 + -6x + -21x + 12x2 = 12 + 21x + -12 + -21x Combine like terms: -6x + -21x = -27x -24 + -27x + 12x2 = 12 + 21x + -12 + -21x Reorder the terms: -24 + -27x + 12x2 = 12 + -12 + 21x + -21x Combine like terms: 12 + -12 = 0 -24 + -27x + 12x2 = 0 + 21x + -21x -24 + -27x + 12x2 = 21x + -21x Combine like terms: 21x + -21x = 0 -24 + -27x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-8 + -9x + 4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-8 + -9x + 4x2)' equal to zero and attempt to solve: Simplifying -8 + -9x + 4x2 = 0 Solving -8 + -9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2 + -2.25x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -2.25x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -2.25x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2.25x + x2 = 0 + 2 -2.25x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -2.25x + x2 = 2 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 = 2 + 1.265625 Reorder the terms: 1.265625 + -2.25x + x2 = 2 + 1.265625 Combine like terms: 2 + 1.265625 = 3.265625 1.265625 + -2.25x + x2 = 3.265625 Factor a perfect square on the left side: (x + -1.125)(x + -1.125) = 3.265625 Calculate the square root of the right side: 1.807104037 Break this problem into two subproblems by setting (x + -1.125) equal to 1.807104037 and -1.807104037.Subproblem 1
x + -1.125 = 1.807104037 Simplifying x + -1.125 = 1.807104037 Reorder the terms: -1.125 + x = 1.807104037 Solving -1.125 + x = 1.807104037 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 = 1.807104037 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 1.807104037 + 1.125 x = 1.807104037 + 1.125 Combine like terms: 1.807104037 + 1.125 = 2.932104037 x = 2.932104037 Simplifying x = 2.932104037Subproblem 2
x + -1.125 = -1.807104037 Simplifying x + -1.125 = -1.807104037 Reorder the terms: -1.125 + x = -1.807104037 Solving -1.125 + x = -1.807104037 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 = -1.807104037 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -1.807104037 + 1.125 x = -1.807104037 + 1.125 Combine like terms: -1.807104037 + 1.125 = -0.682104037 x = -0.682104037 Simplifying x = -0.682104037Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.932104037, -0.682104037}Solution
x = {2.932104037, -0.682104037}
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