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Simplifying 0 = 25x2 + 5x + 1 Reorder the terms: 0 = 1 + 5x + 25x2 Solving 0 = 1 + 5x + 25x2 Solving for variable 'x'. Combine like terms: 0 + -1 = -1 -1 + -5x + -25x2 = 1 + 5x + 25x2 + -1 + -5x + -25x2 Reorder the terms: -1 + -5x + -25x2 = 1 + -1 + 5x + -5x + 25x2 + -25x2 Combine like terms: 1 + -1 = 0 -1 + -5x + -25x2 = 0 + 5x + -5x + 25x2 + -25x2 -1 + -5x + -25x2 = 5x + -5x + 25x2 + -25x2 Combine like terms: 5x + -5x = 0 -1 + -5x + -25x2 = 0 + 25x2 + -25x2 -1 + -5x + -25x2 = 25x2 + -25x2 Combine like terms: 25x2 + -25x2 = 0 -1 + -5x + -25x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 5x + 25x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 5x + 25x2)' equal to zero and attempt to solve: Simplifying 1 + 5x + 25x2 = 0 Solving 1 + 5x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.04 + 0.2x + x2 = 0 Move the constant term to the right: Add '-0.04' to each side of the equation. 0.04 + 0.2x + -0.04 + x2 = 0 + -0.04 Reorder the terms: 0.04 + -0.04 + 0.2x + x2 = 0 + -0.04 Combine like terms: 0.04 + -0.04 = 0.00 0.00 + 0.2x + x2 = 0 + -0.04 0.2x + x2 = 0 + -0.04 Combine like terms: 0 + -0.04 = -0.04 0.2x + x2 = -0.04 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 = -0.04 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = -0.04 + 0.01 Combine like terms: -0.04 + 0.01 = -0.03 0.01 + 0.2x + x2 = -0.03 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = -0.03 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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