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Simplifying 0 = 2x2 + 56x + 784 Reorder the terms: 0 = 784 + 56x + 2x2 Solving 0 = 784 + 56x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -784 = -784 -784 + -56x + -2x2 = 784 + 56x + 2x2 + -784 + -56x + -2x2 Reorder the terms: -784 + -56x + -2x2 = 784 + -784 + 56x + -56x + 2x2 + -2x2 Combine like terms: 784 + -784 = 0 -784 + -56x + -2x2 = 0 + 56x + -56x + 2x2 + -2x2 -784 + -56x + -2x2 = 56x + -56x + 2x2 + -2x2 Combine like terms: 56x + -56x = 0 -784 + -56x + -2x2 = 0 + 2x2 + -2x2 -784 + -56x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -784 + -56x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(392 + 28x + x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(392 + 28x + x2)' equal to zero and attempt to solve: Simplifying 392 + 28x + x2 = 0 Solving 392 + 28x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-392' to each side of the equation. 392 + 28x + -392 + x2 = 0 + -392 Reorder the terms: 392 + -392 + 28x + x2 = 0 + -392 Combine like terms: 392 + -392 = 0 0 + 28x + x2 = 0 + -392 28x + x2 = 0 + -392 Combine like terms: 0 + -392 = -392 28x + x2 = -392 The x term is 28x. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28x + 196 + x2 = -392 + 196 Reorder the terms: 196 + 28x + x2 = -392 + 196 Combine like terms: -392 + 196 = -196 196 + 28x + x2 = -196 Factor a perfect square on the left side: (x + 14)(x + 14) = -196 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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