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Simplifying 8x(7x + 7) = 2x + -34 Reorder the terms: 8x(7 + 7x) = 2x + -34 (7 * 8x + 7x * 8x) = 2x + -34 (56x + 56x2) = 2x + -34 Reorder the terms: 56x + 56x2 = -34 + 2x Solving 56x + 56x2 = -34 + 2x Solving for variable 'x'. Reorder the terms: 34 + 56x + -2x + 56x2 = -34 + 2x + 34 + -2x Combine like terms: 56x + -2x = 54x 34 + 54x + 56x2 = -34 + 2x + 34 + -2x Reorder the terms: 34 + 54x + 56x2 = -34 + 34 + 2x + -2x Combine like terms: -34 + 34 = 0 34 + 54x + 56x2 = 0 + 2x + -2x 34 + 54x + 56x2 = 2x + -2x Combine like terms: 2x + -2x = 0 34 + 54x + 56x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(17 + 27x + 28x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(17 + 27x + 28x2)' equal to zero and attempt to solve: Simplifying 17 + 27x + 28x2 = 0 Solving 17 + 27x + 28x2 = 0 Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. 0.6071428571 + 0.9642857143x + x2 = 0 Move the constant term to the right: Add '-0.6071428571' to each side of the equation. 0.6071428571 + 0.9642857143x + -0.6071428571 + x2 = 0 + -0.6071428571 Reorder the terms: 0.6071428571 + -0.6071428571 + 0.9642857143x + x2 = 0 + -0.6071428571 Combine like terms: 0.6071428571 + -0.6071428571 = 0.0000000000 0.0000000000 + 0.9642857143x + x2 = 0 + -0.6071428571 0.9642857143x + x2 = 0 + -0.6071428571 Combine like terms: 0 + -0.6071428571 = -0.6071428571 0.9642857143x + x2 = -0.6071428571 The x term is 0.9642857143x. Take half its coefficient (0.4821428572). Square it (0.2324617347) and add it to both sides. Add '0.2324617347' to each side of the equation. 0.9642857143x + 0.2324617347 + x2 = -0.6071428571 + 0.2324617347 Reorder the terms: 0.2324617347 + 0.9642857143x + x2 = -0.6071428571 + 0.2324617347 Combine like terms: -0.6071428571 + 0.2324617347 = -0.3746811224 0.2324617347 + 0.9642857143x + x2 = -0.3746811224 Factor a perfect square on the left side: (x + 0.4821428572)(x + 0.4821428572) = -0.3746811224 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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