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Simplifying (5x2 + -7x + -8) + (2x2 + -3x + 7) + -1(x2 + -4x + -3) = 0 Reorder the terms: (-8 + -7x + 5x2) + (2x2 + -3x + 7) + -1(x2 + -4x + -3) = 0 Remove parenthesis around (-8 + -7x + 5x2) -8 + -7x + 5x2 + (2x2 + -3x + 7) + -1(x2 + -4x + -3) = 0 Reorder the terms: -8 + -7x + 5x2 + (7 + -3x + 2x2) + -1(x2 + -4x + -3) = 0 Remove parenthesis around (7 + -3x + 2x2) -8 + -7x + 5x2 + 7 + -3x + 2x2 + -1(x2 + -4x + -3) = 0 Reorder the terms: -8 + -7x + 5x2 + 7 + -3x + 2x2 + -1(-3 + -4x + x2) = 0 -8 + -7x + 5x2 + 7 + -3x + 2x2 + (-3 * -1 + -4x * -1 + x2 * -1) = 0 -8 + -7x + 5x2 + 7 + -3x + 2x2 + (3 + 4x + -1x2) = 0 Reorder the terms: -8 + 7 + 3 + -7x + -3x + 4x + 5x2 + 2x2 + -1x2 = 0 Combine like terms: -8 + 7 = -1 -1 + 3 + -7x + -3x + 4x + 5x2 + 2x2 + -1x2 = 0 Combine like terms: -1 + 3 = 2 2 + -7x + -3x + 4x + 5x2 + 2x2 + -1x2 = 0 Combine like terms: -7x + -3x = -10x 2 + -10x + 4x + 5x2 + 2x2 + -1x2 = 0 Combine like terms: -10x + 4x = -6x 2 + -6x + 5x2 + 2x2 + -1x2 = 0 Combine like terms: 5x2 + 2x2 = 7x2 2 + -6x + 7x2 + -1x2 = 0 Combine like terms: 7x2 + -1x2 = 6x2 2 + -6x + 6x2 = 0 Solving 2 + -6x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -3x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -3x + 3x2)' equal to zero and attempt to solve: Simplifying 1 + -3x + 3x2 = 0 Solving 1 + -3x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.3333333333 + -1x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -1x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -1x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -1x + x2 = 0 + -0.3333333333 -1x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -1x + x2 = -0.3333333333 The x term is -1x. 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. -1x + 0.25 + x2 = -0.3333333333 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.3333333333 + 0.25 Combine like terms: -0.3333333333 + 0.25 = -0.0833333333 0.25 + -1x + x2 = -0.0833333333 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = -0.0833333333 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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