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Simplifying 25x2 + -100 + 100 = (5x + -10) Reorder the terms: -100 + 100 + 25x2 = (5x + -10) Combine like terms: -100 + 100 = 0 0 + 25x2 = (5x + -10) 25x2 = (5x + -10) Reorder the terms: 25x2 = (-10 + 5x) Remove parenthesis around (-10 + 5x) 25x2 = -10 + 5x Solving 25x2 = -10 + 5x Solving for variable 'x'. Reorder the terms: 10 + -5x + 25x2 = -10 + 5x + 10 + -5x Reorder the terms: 10 + -5x + 25x2 = -10 + 10 + 5x + -5x Combine like terms: -10 + 10 = 0 10 + -5x + 25x2 = 0 + 5x + -5x 10 + -5x + 25x2 = 5x + -5x Combine like terms: 5x + -5x = 0 10 + -5x + 25x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(2 + -1x + 5x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(2 + -1x + 5x2)' equal to zero and attempt to solve: Simplifying 2 + -1x + 5x2 = 0 Solving 2 + -1x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + -0.2x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -0.2x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -0.2x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -0.2x + x2 = 0 + -0.4 -0.2x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -0.2x + x2 = -0.4 The x term is -0.2x. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2x + 0.01 + x2 = -0.4 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = -0.4 + 0.01 Combine like terms: -0.4 + 0.01 = -0.39 0.01 + -0.2x + x2 = -0.39 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = -0.39 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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