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Simplifying (2x + -5)(2x + -5) = -49 Reorder the terms: (-5 + 2x)(2x + -5) = -49 Reorder the terms: (-5 + 2x)(-5 + 2x) = -49 Multiply (-5 + 2x) * (-5 + 2x) (-5(-5 + 2x) + 2x * (-5 + 2x)) = -49 ((-5 * -5 + 2x * -5) + 2x * (-5 + 2x)) = -49 ((25 + -10x) + 2x * (-5 + 2x)) = -49 (25 + -10x + (-5 * 2x + 2x * 2x)) = -49 (25 + -10x + (-10x + 4x2)) = -49 Combine like terms: -10x + -10x = -20x (25 + -20x + 4x2) = -49 Solving 25 + -20x + 4x2 = -49 Solving for variable 'x'. Reorder the terms: 25 + 49 + -20x + 4x2 = -49 + 49 Combine like terms: 25 + 49 = 74 74 + -20x + 4x2 = -49 + 49 Combine like terms: -49 + 49 = 0 74 + -20x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(37 + -10x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(37 + -10x + 2x2)' equal to zero and attempt to solve: Simplifying 37 + -10x + 2x2 = 0 Solving 37 + -10x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 18.5 + -5x + x2 = 0 Move the constant term to the right: Add '-18.5' to each side of the equation. 18.5 + -5x + -18.5 + x2 = 0 + -18.5 Reorder the terms: 18.5 + -18.5 + -5x + x2 = 0 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + -5x + x2 = 0 + -18.5 -5x + x2 = 0 + -18.5 Combine like terms: 0 + -18.5 = -18.5 -5x + x2 = -18.5 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -18.5 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -18.5 + 6.25 Combine like terms: -18.5 + 6.25 = -12.25 6.25 + -5x + x2 = -12.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = -12.25 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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