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Simplifying 16x2 + 28x + 200 = 0 Reorder the terms: 200 + 28x + 16x2 = 0 Solving 200 + 28x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(50 + 7x + 4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(50 + 7x + 4x2)' equal to zero and attempt to solve: Simplifying 50 + 7x + 4x2 = 0 Solving 50 + 7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 12.5 + 1.75x + x2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + 1.75x + -12.5 + x2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + 1.75x + x2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + 1.75x + x2 = 0 + -12.5 1.75x + x2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 1.75x + x2 = -12.5 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 = -12.5 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = -12.5 + 0.765625 Combine like terms: -12.5 + 0.765625 = -11.734375 0.765625 + 1.75x + x2 = -11.734375 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = -11.734375 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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