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Simplifying -6(4x + 1) * 7x + 9(x + -3) = 4 Reorder the terms: -6(1 + 4x) * 7x + 9(x + -3) = 4 Reorder the terms for easier multiplication: -6 * 7x(1 + 4x) + 9(x + -3) = 4 Multiply -6 * 7 -42x(1 + 4x) + 9(x + -3) = 4 (1 * -42x + 4x * -42x) + 9(x + -3) = 4 (-42x + -168x2) + 9(x + -3) = 4 Reorder the terms: -42x + -168x2 + 9(-3 + x) = 4 -42x + -168x2 + (-3 * 9 + x * 9) = 4 -42x + -168x2 + (-27 + 9x) = 4 Reorder the terms: -27 + -42x + 9x + -168x2 = 4 Combine like terms: -42x + 9x = -33x -27 + -33x + -168x2 = 4 Solving -27 + -33x + -168x2 = 4 Solving for variable 'x'. Reorder the terms: -27 + -4 + -33x + -168x2 = 4 + -4 Combine like terms: -27 + -4 = -31 -31 + -33x + -168x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -31 + -33x + -168x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(31 + 33x + 168x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(31 + 33x + 168x2)' equal to zero and attempt to solve: Simplifying 31 + 33x + 168x2 = 0 Solving 31 + 33x + 168x2 = 0 Begin completing the square. Divide all terms by 168 the coefficient of the squared term: Divide each side by '168'. 0.1845238095 + 0.1964285714x + x2 = 0 Move the constant term to the right: Add '-0.1845238095' to each side of the equation. 0.1845238095 + 0.1964285714x + -0.1845238095 + x2 = 0 + -0.1845238095 Reorder the terms: 0.1845238095 + -0.1845238095 + 0.1964285714x + x2 = 0 + -0.1845238095 Combine like terms: 0.1845238095 + -0.1845238095 = 0.0000000000 0.0000000000 + 0.1964285714x + x2 = 0 + -0.1845238095 0.1964285714x + x2 = 0 + -0.1845238095 Combine like terms: 0 + -0.1845238095 = -0.1845238095 0.1964285714x + x2 = -0.1845238095 The x term is 0.1964285714x. Take half its coefficient (0.0982142857). Square it (0.009646045916) and add it to both sides. Add '0.009646045916' to each side of the equation. 0.1964285714x + 0.009646045916 + x2 = -0.1845238095 + 0.009646045916 Reorder the terms: 0.009646045916 + 0.1964285714x + x2 = -0.1845238095 + 0.009646045916 Combine like terms: -0.1845238095 + 0.009646045916 = -0.174877763584 0.009646045916 + 0.1964285714x + x2 = -0.174877763584 Factor a perfect square on the left side: (x + 0.0982142857)(x + 0.0982142857) = -0.174877763584 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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