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Simplifying 6(3x + -7) + -12 + -4x = 9x(7x + 6) Reorder the terms: 6(-7 + 3x) + -12 + -4x = 9x(7x + 6) (-7 * 6 + 3x * 6) + -12 + -4x = 9x(7x + 6) (-42 + 18x) + -12 + -4x = 9x(7x + 6) Reorder the terms: -42 + -12 + 18x + -4x = 9x(7x + 6) Combine like terms: -42 + -12 = -54 -54 + 18x + -4x = 9x(7x + 6) Combine like terms: 18x + -4x = 14x -54 + 14x = 9x(7x + 6) Reorder the terms: -54 + 14x = 9x(6 + 7x) -54 + 14x = (6 * 9x + 7x * 9x) -54 + 14x = (54x + 63x2) Solving -54 + 14x = 54x + 63x2 Solving for variable 'x'. Combine like terms: 14x + -54x = -40x -54 + -40x + -63x2 = 54x + 63x2 + -54x + -63x2 Reorder the terms: -54 + -40x + -63x2 = 54x + -54x + 63x2 + -63x2 Combine like terms: 54x + -54x = 0 -54 + -40x + -63x2 = 0 + 63x2 + -63x2 -54 + -40x + -63x2 = 63x2 + -63x2 Combine like terms: 63x2 + -63x2 = 0 -54 + -40x + -63x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(54 + 40x + 63x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(54 + 40x + 63x2)' equal to zero and attempt to solve: Simplifying 54 + 40x + 63x2 = 0 Solving 54 + 40x + 63x2 = 0 Begin completing the square. Divide all terms by 63 the coefficient of the squared term: Divide each side by '63'. 0.8571428571 + 0.6349206349x + x2 = 0 Move the constant term to the right: Add '-0.8571428571' to each side of the equation. 0.8571428571 + 0.6349206349x + -0.8571428571 + x2 = 0 + -0.8571428571 Reorder the terms: 0.8571428571 + -0.8571428571 + 0.6349206349x + x2 = 0 + -0.8571428571 Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000 0.0000000000 + 0.6349206349x + x2 = 0 + -0.8571428571 0.6349206349x + x2 = 0 + -0.8571428571 Combine like terms: 0 + -0.8571428571 = -0.8571428571 0.6349206349x + x2 = -0.8571428571 The x term is 0.6349206349x. Take half its coefficient (0.3174603175). Square it (0.1007810532) and add it to both sides. Add '0.1007810532' to each side of the equation. 0.6349206349x + 0.1007810532 + x2 = -0.8571428571 + 0.1007810532 Reorder the terms: 0.1007810532 + 0.6349206349x + x2 = -0.8571428571 + 0.1007810532 Combine like terms: -0.8571428571 + 0.1007810532 = -0.7563618039 0.1007810532 + 0.6349206349x + x2 = -0.7563618039 Factor a perfect square on the left side: (x + 0.3174603175)(x + 0.3174603175) = -0.7563618039 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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