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Simplifying (5x2 + -4x + 3) + (-1x2 + 2x + 5) = 0 Reorder the terms: (3 + -4x + 5x2) + (-1x2 + 2x + 5) = 0 Remove parenthesis around (3 + -4x + 5x2) 3 + -4x + 5x2 + (-1x2 + 2x + 5) = 0 Reorder the terms: 3 + -4x + 5x2 + (5 + 2x + -1x2) = 0 Remove parenthesis around (5 + 2x + -1x2) 3 + -4x + 5x2 + 5 + 2x + -1x2 = 0 Reorder the terms: 3 + 5 + -4x + 2x + 5x2 + -1x2 = 0 Combine like terms: 3 + 5 = 8 8 + -4x + 2x + 5x2 + -1x2 = 0 Combine like terms: -4x + 2x = -2x 8 + -2x + 5x2 + -1x2 = 0 Combine like terms: 5x2 + -1x2 = 4x2 8 + -2x + 4x2 = 0 Solving 8 + -2x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -1x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -1x + 2x2)' equal to zero and attempt to solve: Simplifying 4 + -1x + 2x2 = 0 Solving 4 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2 + -0.5x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -0.5x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -0.5x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -0.5x + x2 = 0 + -2 -0.5x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -0.5x + x2 = -2 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = -2 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = -2 + 0.0625 Combine like terms: -2 + 0.0625 = -1.9375 0.0625 + -0.5x + x2 = -1.9375 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = -1.9375 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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