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Simplifying 4x2 + 25 + 20 = -2x + 5 Reorder the terms: 25 + 20 + 4x2 = -2x + 5 Combine like terms: 25 + 20 = 45 45 + 4x2 = -2x + 5 Reorder the terms: 45 + 4x2 = 5 + -2x Solving 45 + 4x2 = 5 + -2x Solving for variable 'x'. Reorder the terms: 45 + -5 + 2x + 4x2 = 5 + -2x + -5 + 2x Combine like terms: 45 + -5 = 40 40 + 2x + 4x2 = 5 + -2x + -5 + 2x Reorder the terms: 40 + 2x + 4x2 = 5 + -5 + -2x + 2x Combine like terms: 5 + -5 = 0 40 + 2x + 4x2 = 0 + -2x + 2x 40 + 2x + 4x2 = -2x + 2x Combine like terms: -2x + 2x = 0 40 + 2x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(20 + x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(20 + x + 2x2)' equal to zero and attempt to solve: Simplifying 20 + x + 2x2 = 0 Solving 20 + x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 10 + 0.5x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + 0.5x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + 0.5x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 0.5x + x2 = 0 + -10 0.5x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 0.5x + x2 = -10 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5x + 0.25 + x2 = -10 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = -10 + 0.25 Combine like terms: -10 + 0.25 = -9.75 0.25 + 0.5x + x2 = -9.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -9.75 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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