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Simplifying (6x + 2)(8x + -14) = (48x + -12) Reorder the terms: (2 + 6x)(8x + -14) = (48x + -12) Reorder the terms: (2 + 6x)(-14 + 8x) = (48x + -12) Multiply (2 + 6x) * (-14 + 8x) (2(-14 + 8x) + 6x * (-14 + 8x)) = (48x + -12) ((-14 * 2 + 8x * 2) + 6x * (-14 + 8x)) = (48x + -12) ((-28 + 16x) + 6x * (-14 + 8x)) = (48x + -12) (-28 + 16x + (-14 * 6x + 8x * 6x)) = (48x + -12) (-28 + 16x + (-84x + 48x2)) = (48x + -12) Combine like terms: 16x + -84x = -68x (-28 + -68x + 48x2) = (48x + -12) Reorder the terms: -28 + -68x + 48x2 = (-12 + 48x) Remove parenthesis around (-12 + 48x) -28 + -68x + 48x2 = -12 + 48x Solving -28 + -68x + 48x2 = -12 + 48x Solving for variable 'x'. Reorder the terms: -28 + 12 + -68x + -48x + 48x2 = -12 + 48x + 12 + -48x Combine like terms: -28 + 12 = -16 -16 + -68x + -48x + 48x2 = -12 + 48x + 12 + -48x Combine like terms: -68x + -48x = -116x -16 + -116x + 48x2 = -12 + 48x + 12 + -48x Reorder the terms: -16 + -116x + 48x2 = -12 + 12 + 48x + -48x Combine like terms: -12 + 12 = 0 -16 + -116x + 48x2 = 0 + 48x + -48x -16 + -116x + 48x2 = 48x + -48x Combine like terms: 48x + -48x = 0 -16 + -116x + 48x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-4 + -29x + 12x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-4 + -29x + 12x2)' equal to zero and attempt to solve: Simplifying -4 + -29x + 12x2 = 0 Solving -4 + -29x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.3333333333 + -2.416666667x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -2.416666667x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -2.416666667x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -2.416666667x + x2 = 0 + 0.3333333333 -2.416666667x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -2.416666667x + x2 = 0.3333333333 The x term is -2.416666667x. Take half its coefficient (-1.208333334). Square it (1.460069446) and add it to both sides. Add '1.460069446' to each side of the equation. -2.416666667x + 1.460069446 + x2 = 0.3333333333 + 1.460069446 Reorder the terms: 1.460069446 + -2.416666667x + x2 = 0.3333333333 + 1.460069446 Combine like terms: 0.3333333333 + 1.460069446 = 1.7934027793 1.460069446 + -2.416666667x + x2 = 1.7934027793 Factor a perfect square on the left side: (x + -1.208333334)(x + -1.208333334) = 1.7934027793 Calculate the square root of the right side: 1.339179891 Break this problem into two subproblems by setting (x + -1.208333334) equal to 1.339179891 and -1.339179891.Subproblem 1
x + -1.208333334 = 1.339179891 Simplifying x + -1.208333334 = 1.339179891 Reorder the terms: -1.208333334 + x = 1.339179891 Solving -1.208333334 + x = 1.339179891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.208333334' to each side of the equation. -1.208333334 + 1.208333334 + x = 1.339179891 + 1.208333334 Combine like terms: -1.208333334 + 1.208333334 = 0.000000000 0.000000000 + x = 1.339179891 + 1.208333334 x = 1.339179891 + 1.208333334 Combine like terms: 1.339179891 + 1.208333334 = 2.547513225 x = 2.547513225 Simplifying x = 2.547513225Subproblem 2
x + -1.208333334 = -1.339179891 Simplifying x + -1.208333334 = -1.339179891 Reorder the terms: -1.208333334 + x = -1.339179891 Solving -1.208333334 + x = -1.339179891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.208333334' to each side of the equation. -1.208333334 + 1.208333334 + x = -1.339179891 + 1.208333334 Combine like terms: -1.208333334 + 1.208333334 = 0.000000000 0.000000000 + x = -1.339179891 + 1.208333334 x = -1.339179891 + 1.208333334 Combine like terms: -1.339179891 + 1.208333334 = -0.130846557 x = -0.130846557 Simplifying x = -0.130846557Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.547513225, -0.130846557}Solution
x = {2.547513225, -0.130846557}
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