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Simplifying (3x + -7) + -12 + -4x = 9x(7x + 6) Reorder the terms: (-7 + 3x) + -12 + -4x = 9x(7x + 6) Remove parenthesis around (-7 + 3x) -7 + 3x + -12 + -4x = 9x(7x + 6) Reorder the terms: -7 + -12 + 3x + -4x = 9x(7x + 6) Combine like terms: -7 + -12 = -19 -19 + 3x + -4x = 9x(7x + 6) Combine like terms: 3x + -4x = -1x -19 + -1x = 9x(7x + 6) Reorder the terms: -19 + -1x = 9x(6 + 7x) -19 + -1x = (6 * 9x + 7x * 9x) -19 + -1x = (54x + 63x2) Solving -19 + -1x = 54x + 63x2 Solving for variable 'x'. Combine like terms: -1x + -54x = -55x -19 + -55x + -63x2 = 54x + 63x2 + -54x + -63x2 Reorder the terms: -19 + -55x + -63x2 = 54x + -54x + 63x2 + -63x2 Combine like terms: 54x + -54x = 0 -19 + -55x + -63x2 = 0 + 63x2 + -63x2 -19 + -55x + -63x2 = 63x2 + -63x2 Combine like terms: 63x2 + -63x2 = 0 -19 + -55x + -63x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(19 + 55x + 63x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(19 + 55x + 63x2)' equal to zero and attempt to solve: Simplifying 19 + 55x + 63x2 = 0 Solving 19 + 55x + 63x2 = 0 Begin completing the square. Divide all terms by 63 the coefficient of the squared term: Divide each side by '63'. 0.3015873016 + 0.873015873x + x2 = 0 Move the constant term to the right: Add '-0.3015873016' to each side of the equation. 0.3015873016 + 0.873015873x + -0.3015873016 + x2 = 0 + -0.3015873016 Reorder the terms: 0.3015873016 + -0.3015873016 + 0.873015873x + x2 = 0 + -0.3015873016 Combine like terms: 0.3015873016 + -0.3015873016 = 0.0000000000 0.0000000000 + 0.873015873x + x2 = 0 + -0.3015873016 0.873015873x + x2 = 0 + -0.3015873016 Combine like terms: 0 + -0.3015873016 = -0.3015873016 0.873015873x + x2 = -0.3015873016 The x term is 0.873015873x. Take half its coefficient (0.4365079365). Square it (0.1905391786) and add it to both sides. Add '0.1905391786' to each side of the equation. 0.873015873x + 0.1905391786 + x2 = -0.3015873016 + 0.1905391786 Reorder the terms: 0.1905391786 + 0.873015873x + x2 = -0.3015873016 + 0.1905391786 Combine like terms: -0.3015873016 + 0.1905391786 = -0.111048123 0.1905391786 + 0.873015873x + x2 = -0.111048123 Factor a perfect square on the left side: (x + 0.4365079365)(x + 0.4365079365) = -0.111048123 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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