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Simplifying 8x2 + 14x + 40 = 0 Reorder the terms: 40 + 14x + 8x2 = 0 Solving 40 + 14x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(20 + 7x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(20 + 7x + 4x2)' equal to zero and attempt to solve: Simplifying 20 + 7x + 4x2 = 0 Solving 20 + 7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 5 + 1.75x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + 1.75x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 1.75x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 1.75x + x2 = 0 + -5 1.75x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 1.75x + x2 = -5 The x term is 1.75x. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x + 0.765625 + x2 = -5 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = -5 + 0.765625 Combine like terms: -5 + 0.765625 = -4.234375 0.765625 + 1.75x + x2 = -4.234375 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = -4.234375 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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