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Simplifying 14x2 + 84x + 12 = 28x + -84 Reorder the terms: 12 + 84x + 14x2 = 28x + -84 Reorder the terms: 12 + 84x + 14x2 = -84 + 28x Solving 12 + 84x + 14x2 = -84 + 28x Solving for variable 'x'. Reorder the terms: 12 + 84 + 84x + -28x + 14x2 = -84 + 28x + 84 + -28x Combine like terms: 12 + 84 = 96 96 + 84x + -28x + 14x2 = -84 + 28x + 84 + -28x Combine like terms: 84x + -28x = 56x 96 + 56x + 14x2 = -84 + 28x + 84 + -28x Reorder the terms: 96 + 56x + 14x2 = -84 + 84 + 28x + -28x Combine like terms: -84 + 84 = 0 96 + 56x + 14x2 = 0 + 28x + -28x 96 + 56x + 14x2 = 28x + -28x Combine like terms: 28x + -28x = 0 96 + 56x + 14x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(48 + 28x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(48 + 28x + 7x2)' equal to zero and attempt to solve: Simplifying 48 + 28x + 7x2 = 0 Solving 48 + 28x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 6.857142857 + 4x + x2 = 0 Move the constant term to the right: Add '-6.857142857' to each side of the equation. 6.857142857 + 4x + -6.857142857 + x2 = 0 + -6.857142857 Reorder the terms: 6.857142857 + -6.857142857 + 4x + x2 = 0 + -6.857142857 Combine like terms: 6.857142857 + -6.857142857 = 0.000000000 0.000000000 + 4x + x2 = 0 + -6.857142857 4x + x2 = 0 + -6.857142857 Combine like terms: 0 + -6.857142857 = -6.857142857 4x + x2 = -6.857142857 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -6.857142857 + 4 Reorder the terms: 4 + 4x + x2 = -6.857142857 + 4 Combine like terms: -6.857142857 + 4 = -2.857142857 4 + 4x + x2 = -2.857142857 Factor a perfect square on the left side: (x + 2)(x + 2) = -2.857142857 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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