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Simplifying (-7x2 + 4x + -5) + -1(x2 + 5x + -6) + (x2 + -3) = 0 Reorder the terms: (-5 + 4x + -7x2) + -1(x2 + 5x + -6) + (x2 + -3) = 0 Remove parenthesis around (-5 + 4x + -7x2) -5 + 4x + -7x2 + -1(x2 + 5x + -6) + (x2 + -3) = 0 Reorder the terms: -5 + 4x + -7x2 + -1(-6 + 5x + x2) + (x2 + -3) = 0 -5 + 4x + -7x2 + (-6 * -1 + 5x * -1 + x2 * -1) + (x2 + -3) = 0 -5 + 4x + -7x2 + (6 + -5x + -1x2) + (x2 + -3) = 0 Reorder the terms: -5 + 4x + -7x2 + 6 + -5x + -1x2 + (-3 + x2) = 0 Remove parenthesis around (-3 + x2) -5 + 4x + -7x2 + 6 + -5x + -1x2 + -3 + x2 = 0 Reorder the terms: -5 + 6 + -3 + 4x + -5x + -7x2 + -1x2 + x2 = 0 Combine like terms: -5 + 6 = 1 1 + -3 + 4x + -5x + -7x2 + -1x2 + x2 = 0 Combine like terms: 1 + -3 = -2 -2 + 4x + -5x + -7x2 + -1x2 + x2 = 0 Combine like terms: 4x + -5x = -1x -2 + -1x + -7x2 + -1x2 + x2 = 0 Combine like terms: -7x2 + -1x2 = -8x2 -2 + -1x + -8x2 + x2 = 0 Combine like terms: -8x2 + x2 = -7x2 -2 + -1x + -7x2 = 0 Solving -2 + -1x + -7x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + x + 7x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + x + 7x2)' equal to zero and attempt to solve: Simplifying 2 + x + 7x2 = 0 Solving 2 + x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.2857142857 + 0.1428571429x + x2 = 0 Move the constant term to the right: Add '-0.2857142857' to each side of the equation. 0.2857142857 + 0.1428571429x + -0.2857142857 + x2 = 0 + -0.2857142857 Reorder the terms: 0.2857142857 + -0.2857142857 + 0.1428571429x + x2 = 0 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + 0.1428571429x + x2 = 0 + -0.2857142857 0.1428571429x + x2 = 0 + -0.2857142857 Combine like terms: 0 + -0.2857142857 = -0.2857142857 0.1428571429x + x2 = -0.2857142857 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. 0.1428571429x + 0.25 + x2 = -0.2857142857 + 0.25 Reorder the terms: 0.25 + 0.1428571429x + x2 = -0.2857142857 + 0.25 Combine like terms: -0.2857142857 + 0.25 = -0.0357142857 0.25 + 0.1428571429x + x2 = -0.0357142857 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.0357142857 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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