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Simplifying (8x2 + -8x + 12) + (4x2 + -12x + 14) = 0 Reorder the terms: (12 + -8x + 8x2) + (4x2 + -12x + 14) = 0 Remove parenthesis around (12 + -8x + 8x2) 12 + -8x + 8x2 + (4x2 + -12x + 14) = 0 Reorder the terms: 12 + -8x + 8x2 + (14 + -12x + 4x2) = 0 Remove parenthesis around (14 + -12x + 4x2) 12 + -8x + 8x2 + 14 + -12x + 4x2 = 0 Reorder the terms: 12 + 14 + -8x + -12x + 8x2 + 4x2 = 0 Combine like terms: 12 + 14 = 26 26 + -8x + -12x + 8x2 + 4x2 = 0 Combine like terms: -8x + -12x = -20x 26 + -20x + 8x2 + 4x2 = 0 Combine like terms: 8x2 + 4x2 = 12x2 26 + -20x + 12x2 = 0 Solving 26 + -20x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(13 + -10x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(13 + -10x + 6x2)' equal to zero and attempt to solve: Simplifying 13 + -10x + 6x2 = 0 Solving 13 + -10x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 2.166666667 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '-2.166666667' to each side of the equation. 2.166666667 + -1.666666667x + -2.166666667 + x2 = 0 + -2.166666667 Reorder the terms: 2.166666667 + -2.166666667 + -1.666666667x + x2 = 0 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + -1.666666667x + x2 = 0 + -2.166666667 -1.666666667x + x2 = 0 + -2.166666667 Combine like terms: 0 + -2.166666667 = -2.166666667 -1.666666667x + x2 = -2.166666667 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = -2.166666667 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = -2.166666667 + 0.6944444447 Combine like terms: -2.166666667 + 0.6944444447 = -1.4722222223 0.6944444447 + -1.666666667x + x2 = -1.4722222223 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = -1.4722222223 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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