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Simplifying 0 = 5X2 + 4X + 20 Reorder the terms: 0 = 20 + 4X + 5X2 Solving 0 = 20 + 4X + 5X2 Solving for variable 'X'. Combine like terms: 0 + -20 = -20 -20 + -4X + -5X2 = 20 + 4X + 5X2 + -20 + -4X + -5X2 Reorder the terms: -20 + -4X + -5X2 = 20 + -20 + 4X + -4X + 5X2 + -5X2 Combine like terms: 20 + -20 = 0 -20 + -4X + -5X2 = 0 + 4X + -4X + 5X2 + -5X2 -20 + -4X + -5X2 = 4X + -4X + 5X2 + -5X2 Combine like terms: 4X + -4X = 0 -20 + -4X + -5X2 = 0 + 5X2 + -5X2 -20 + -4X + -5X2 = 5X2 + -5X2 Combine like terms: 5X2 + -5X2 = 0 -20 + -4X + -5X2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(20 + 4X + 5X2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(20 + 4X + 5X2)' equal to zero and attempt to solve: Simplifying 20 + 4X + 5X2 = 0 Solving 20 + 4X + 5X2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 4 + 0.8X + X2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 0.8X + -4 + X2 = 0 + -4 Reorder the terms: 4 + -4 + 0.8X + X2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 0.8X + X2 = 0 + -4 0.8X + X2 = 0 + -4 Combine like terms: 0 + -4 = -4 0.8X + X2 = -4 The X term is 0.8X. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8X + 0.16 + X2 = -4 + 0.16 Reorder the terms: 0.16 + 0.8X + X2 = -4 + 0.16 Combine like terms: -4 + 0.16 = -3.84 0.16 + 0.8X + X2 = -3.84 Factor a perfect square on the left side: (X + 0.4)(X + 0.4) = -3.84 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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