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Simplifying 10x2 + 14x + 284 = 0 Reorder the terms: 284 + 14x + 10x2 = 0 Solving 284 + 14x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(142 + 7x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(142 + 7x + 5x2)' equal to zero and attempt to solve: Simplifying 142 + 7x + 5x2 = 0 Solving 142 + 7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 28.4 + 1.4x + x2 = 0 Move the constant term to the right: Add '-28.4' to each side of the equation. 28.4 + 1.4x + -28.4 + x2 = 0 + -28.4 Reorder the terms: 28.4 + -28.4 + 1.4x + x2 = 0 + -28.4 Combine like terms: 28.4 + -28.4 = 0.0 0.0 + 1.4x + x2 = 0 + -28.4 1.4x + x2 = 0 + -28.4 Combine like terms: 0 + -28.4 = -28.4 1.4x + x2 = -28.4 The x term is 1.4x. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4x + 0.49 + x2 = -28.4 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = -28.4 + 0.49 Combine like terms: -28.4 + 0.49 = -27.91 0.49 + 1.4x + x2 = -27.91 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = -27.91 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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