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Simplifying 0 = 5x2 + 3x + 1 Reorder the terms: 0 = 1 + 3x + 5x2 Solving 0 = 1 + 3x + 5x2 Solving for variable 'x'. Combine like terms: 0 + -1 = -1 -1 + -3x + -5x2 = 1 + 3x + 5x2 + -1 + -3x + -5x2 Reorder the terms: -1 + -3x + -5x2 = 1 + -1 + 3x + -3x + 5x2 + -5x2 Combine like terms: 1 + -1 = 0 -1 + -3x + -5x2 = 0 + 3x + -3x + 5x2 + -5x2 -1 + -3x + -5x2 = 3x + -3x + 5x2 + -5x2 Combine like terms: 3x + -3x = 0 -1 + -3x + -5x2 = 0 + 5x2 + -5x2 -1 + -3x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -1 + -3x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 3x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 3x + 5x2)' equal to zero and attempt to solve: Simplifying 1 + 3x + 5x2 = 0 Solving 1 + 3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + 0.6x + x2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + 0.6x + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + 0.6x + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + 0.6x + x2 = 0 + -0.2 0.6x + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 0.6x + x2 = -0.2 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = -0.2 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = -0.2 + 0.09 Combine like terms: -0.2 + 0.09 = -0.11 0.09 + 0.6x + x2 = -0.11 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = -0.11 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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