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Simplifying (x + 2)(3x + -6) = (3x + -4) Reorder the terms: (2 + x)(3x + -6) = (3x + -4) Reorder the terms: (2 + x)(-6 + 3x) = (3x + -4) Multiply (2 + x) * (-6 + 3x) (2(-6 + 3x) + x(-6 + 3x)) = (3x + -4) ((-6 * 2 + 3x * 2) + x(-6 + 3x)) = (3x + -4) ((-12 + 6x) + x(-6 + 3x)) = (3x + -4) (-12 + 6x + (-6 * x + 3x * x)) = (3x + -4) (-12 + 6x + (-6x + 3x2)) = (3x + -4) Combine like terms: 6x + -6x = 0 (-12 + 0 + 3x2) = (3x + -4) (-12 + 3x2) = (3x + -4) Reorder the terms: -12 + 3x2 = (-4 + 3x) Remove parenthesis around (-4 + 3x) -12 + 3x2 = -4 + 3x Solving -12 + 3x2 = -4 + 3x Solving for variable 'x'. Reorder the terms: -12 + 4 + -3x + 3x2 = -4 + 3x + 4 + -3x Combine like terms: -12 + 4 = -8 -8 + -3x + 3x2 = -4 + 3x + 4 + -3x Reorder the terms: -8 + -3x + 3x2 = -4 + 4 + 3x + -3x Combine like terms: -4 + 4 = 0 -8 + -3x + 3x2 = 0 + 3x + -3x -8 + -3x + 3x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -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}
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