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Simplifying 10x2 + 168x + 784 = 0 Reorder the terms: 784 + 168x + 10x2 = 0 Solving 784 + 168x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(392 + 84x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(392 + 84x + 5x2)' equal to zero and attempt to solve: Simplifying 392 + 84x + 5x2 = 0 Solving 392 + 84x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 78.4 + 16.8x + x2 = 0 Move the constant term to the right: Add '-78.4' to each side of the equation. 78.4 + 16.8x + -78.4 + x2 = 0 + -78.4 Reorder the terms: 78.4 + -78.4 + 16.8x + x2 = 0 + -78.4 Combine like terms: 78.4 + -78.4 = 0.0 0.0 + 16.8x + x2 = 0 + -78.4 16.8x + x2 = 0 + -78.4 Combine like terms: 0 + -78.4 = -78.4 16.8x + x2 = -78.4 The x term is 16.8x. Take half its coefficient (8.4). Square it (70.56) and add it to both sides. Add '70.56' to each side of the equation. 16.8x + 70.56 + x2 = -78.4 + 70.56 Reorder the terms: 70.56 + 16.8x + x2 = -78.4 + 70.56 Combine like terms: -78.4 + 70.56 = -7.84 70.56 + 16.8x + x2 = -7.84 Factor a perfect square on the left side: (x + 8.4)(x + 8.4) = -7.84 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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