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Simplifying 3x = 10x2 + -3x + 2 Reorder the terms: 3x = 2 + -3x + 10x2 Solving 3x = 2 + -3x + 10x2 Solving for variable 'x'. Reorder the terms: -2 + 3x + 3x + -10x2 = 2 + -3x + 10x2 + -2 + 3x + -10x2 Combine like terms: 3x + 3x = 6x -2 + 6x + -10x2 = 2 + -3x + 10x2 + -2 + 3x + -10x2 Reorder the terms: -2 + 6x + -10x2 = 2 + -2 + -3x + 3x + 10x2 + -10x2 Combine like terms: 2 + -2 = 0 -2 + 6x + -10x2 = 0 + -3x + 3x + 10x2 + -10x2 -2 + 6x + -10x2 = -3x + 3x + 10x2 + -10x2 Combine like terms: -3x + 3x = 0 -2 + 6x + -10x2 = 0 + 10x2 + -10x2 -2 + 6x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 -2 + 6x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 3x + -5x2) = 0 Ignore the factor 2.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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