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Simplifying 6x2 + 8x = 4(3x + -20) Reorder the terms: 8x + 6x2 = 4(3x + -20) Reorder the terms: 8x + 6x2 = 4(-20 + 3x) 8x + 6x2 = (-20 * 4 + 3x * 4) 8x + 6x2 = (-80 + 12x) Solving 8x + 6x2 = -80 + 12x Solving for variable 'x'. Reorder the terms: 80 + 8x + -12x + 6x2 = -80 + 12x + 80 + -12x Combine like terms: 8x + -12x = -4x 80 + -4x + 6x2 = -80 + 12x + 80 + -12x Reorder the terms: 80 + -4x + 6x2 = -80 + 80 + 12x + -12x Combine like terms: -80 + 80 = 0 80 + -4x + 6x2 = 0 + 12x + -12x 80 + -4x + 6x2 = 12x + -12x Combine like terms: 12x + -12x = 0 80 + -4x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(40 + -2x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(40 + -2x + 3x2)' equal to zero and attempt to solve: Simplifying 40 + -2x + 3x2 = 0 Solving 40 + -2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 13.33333333 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '-13.33333333' to each side of the equation. 13.33333333 + -0.6666666667x + -13.33333333 + x2 = 0 + -13.33333333 Reorder the terms: 13.33333333 + -13.33333333 + -0.6666666667x + x2 = 0 + -13.33333333 Combine like terms: 13.33333333 + -13.33333333 = 0.00000000 0.00000000 + -0.6666666667x + x2 = 0 + -13.33333333 -0.6666666667x + x2 = 0 + -13.33333333 Combine like terms: 0 + -13.33333333 = -13.33333333 -0.6666666667x + x2 = -13.33333333 The x term is -0.6666666667x. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667x + 0.1111111112 + x2 = -13.33333333 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = -13.33333333 + 0.1111111112 Combine like terms: -13.33333333 + 0.1111111112 = -13.2222222188 0.1111111112 + -0.6666666667x + x2 = -13.2222222188 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = -13.2222222188 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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