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Simplifying -100x + 55x + 3 = 50x2 + -55x + 23 Reorder the terms: 3 + -100x + 55x = 50x2 + -55x + 23 Combine like terms: -100x + 55x = -45x 3 + -45x = 50x2 + -55x + 23 Reorder the terms: 3 + -45x = 23 + -55x + 50x2 Solving 3 + -45x = 23 + -55x + 50x2 Solving for variable 'x'. Reorder the terms: 3 + -23 + -45x + 55x + -50x2 = 23 + -55x + 50x2 + -23 + 55x + -50x2 Combine like terms: 3 + -23 = -20 -20 + -45x + 55x + -50x2 = 23 + -55x + 50x2 + -23 + 55x + -50x2 Combine like terms: -45x + 55x = 10x -20 + 10x + -50x2 = 23 + -55x + 50x2 + -23 + 55x + -50x2 Reorder the terms: -20 + 10x + -50x2 = 23 + -23 + -55x + 55x + 50x2 + -50x2 Combine like terms: 23 + -23 = 0 -20 + 10x + -50x2 = 0 + -55x + 55x + 50x2 + -50x2 -20 + 10x + -50x2 = -55x + 55x + 50x2 + -50x2 Combine like terms: -55x + 55x = 0 -20 + 10x + -50x2 = 0 + 50x2 + -50x2 -20 + 10x + -50x2 = 50x2 + -50x2 Combine like terms: 50x2 + -50x2 = 0 -20 + 10x + -50x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-2 + x + -5x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-2 + x + -5x2)' equal to zero and attempt to solve: Simplifying -2 + x + -5x2 = 0 Solving -2 + x + -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 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 = -0.4 + 0.25 Reorder the terms: 0.25 + -0.2x + x2 = -0.4 + 0.25 Combine like terms: -0.4 + 0.25 = -0.15 0.25 + -0.2x + x2 = -0.15 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.15 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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