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Simplifying (-12x + -9)(24x + 4) = 43 Reorder the terms: (-9 + -12x)(24x + 4) = 43 Reorder the terms: (-9 + -12x)(4 + 24x) = 43 Multiply (-9 + -12x) * (4 + 24x) (-9(4 + 24x) + -12x * (4 + 24x)) = 43 ((4 * -9 + 24x * -9) + -12x * (4 + 24x)) = 43 ((-36 + -216x) + -12x * (4 + 24x)) = 43 (-36 + -216x + (4 * -12x + 24x * -12x)) = 43 (-36 + -216x + (-48x + -288x2)) = 43 Combine like terms: -216x + -48x = -264x (-36 + -264x + -288x2) = 43 Solving -36 + -264x + -288x2 = 43 Solving for variable 'x'. Reorder the terms: -36 + -43 + -264x + -288x2 = 43 + -43 Combine like terms: -36 + -43 = -79 -79 + -264x + -288x2 = 43 + -43 Combine like terms: 43 + -43 = 0 -79 + -264x + -288x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(79 + 264x + 288x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(79 + 264x + 288x2)' equal to zero and attempt to solve: Simplifying 79 + 264x + 288x2 = 0 Solving 79 + 264x + 288x2 = 0 Begin completing the square. Divide all terms by 288 the coefficient of the squared term: Divide each side by '288'. 0.2743055556 + 0.9166666667x + x2 = 0 Move the constant term to the right: Add '-0.2743055556' to each side of the equation. 0.2743055556 + 0.9166666667x + -0.2743055556 + x2 = 0 + -0.2743055556 Reorder the terms: 0.2743055556 + -0.2743055556 + 0.9166666667x + x2 = 0 + -0.2743055556 Combine like terms: 0.2743055556 + -0.2743055556 = 0.0000000000 0.0000000000 + 0.9166666667x + x2 = 0 + -0.2743055556 0.9166666667x + x2 = 0 + -0.2743055556 Combine like terms: 0 + -0.2743055556 = -0.2743055556 0.9166666667x + x2 = -0.2743055556 The x term is 0.9166666667x. Take half its coefficient (0.4583333334). Square it (0.2100694445) and add it to both sides. Add '0.2100694445' to each side of the equation. 0.9166666667x + 0.2100694445 + x2 = -0.2743055556 + 0.2100694445 Reorder the terms: 0.2100694445 + 0.9166666667x + x2 = -0.2743055556 + 0.2100694445 Combine like terms: -0.2743055556 + 0.2100694445 = -0.0642361111 0.2100694445 + 0.9166666667x + x2 = -0.0642361111 Factor a perfect square on the left side: (x + 0.4583333334)(x + 0.4583333334) = -0.0642361111 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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