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Simplifying 4x(-7x + 2) = 24 Reorder the terms: 4x(2 + -7x) = 24 (2 * 4x + -7x * 4x) = 24 (8x + -28x2) = 24 Solving 8x + -28x2 = 24 Solving for variable 'x'. Reorder the terms: -24 + 8x + -28x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + 8x + -28x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-6 + 2x + -7x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-6 + 2x + -7x2)' equal to zero and attempt to solve: Simplifying -6 + 2x + -7x2 = 0 Solving -6 + 2x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. 0.8571428571 + -0.2857142857x + x2 = 0 Move the constant term to the right: Add '-0.8571428571' to each side of the equation. 0.8571428571 + -0.2857142857x + -0.8571428571 + x2 = 0 + -0.8571428571 Reorder the terms: 0.8571428571 + -0.8571428571 + -0.2857142857x + x2 = 0 + -0.8571428571 Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000 0.0000000000 + -0.2857142857x + x2 = 0 + -0.8571428571 -0.2857142857x + x2 = 0 + -0.8571428571 Combine like terms: 0 + -0.8571428571 = -0.8571428571 -0.2857142857x + x2 = -0.8571428571 The x term is -0.2857142857x. Take half its coefficient (-0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. -0.2857142857x + 0.02040816328 + x2 = -0.8571428571 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857x + x2 = -0.8571428571 + 0.02040816328 Combine like terms: -0.8571428571 + 0.02040816328 = -0.83673469382 0.02040816328 + -0.2857142857x + x2 = -0.83673469382 Factor a perfect square on the left side: (x + -0.1428571429)(x + -0.1428571429) = -0.83673469382 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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