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Simplifying 10x2 = -6 + -2x Solving 10x2 = -6 + -2x Solving for variable 'x'. Reorder the terms: 6 + 2x + 10x2 = -6 + -2x + 6 + 2x Reorder the terms: 6 + 2x + 10x2 = -6 + 6 + -2x + 2x Combine like terms: -6 + 6 = 0 6 + 2x + 10x2 = 0 + -2x + 2x 6 + 2x + 10x2 = -2x + 2x Combine like terms: -2x + 2x = 0 6 + 2x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + x + 5x2)' equal to zero and attempt to solve: Simplifying 3 + x + 5x2 = 0 Solving 3 + x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.6 + 0.2x + x2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + 0.2x + -0.6 + x2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + 0.2x + x2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + 0.2x + x2 = 0 + -0.6 0.2x + x2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 0.2x + x2 = -0.6 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. 0.2x + 0.25 + x2 = -0.6 + 0.25 Reorder the terms: 0.25 + 0.2x + x2 = -0.6 + 0.25 Combine like terms: -0.6 + 0.25 = -0.35 0.25 + 0.2x + x2 = -0.35 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.35 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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