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Simplifying (5x2 + 3x + -6) + (-7x2 + -5x + 1) = 0 Reorder the terms: (-6 + 3x + 5x2) + (-7x2 + -5x + 1) = 0 Remove parenthesis around (-6 + 3x + 5x2) -6 + 3x + 5x2 + (-7x2 + -5x + 1) = 0 Reorder the terms: -6 + 3x + 5x2 + (1 + -5x + -7x2) = 0 Remove parenthesis around (1 + -5x + -7x2) -6 + 3x + 5x2 + 1 + -5x + -7x2 = 0 Reorder the terms: -6 + 1 + 3x + -5x + 5x2 + -7x2 = 0 Combine like terms: -6 + 1 = -5 -5 + 3x + -5x + 5x2 + -7x2 = 0 Combine like terms: 3x + -5x = -2x -5 + -2x + 5x2 + -7x2 = 0 Combine like terms: 5x2 + -7x2 = -2x2 -5 + -2x + -2x2 = 0 Solving -5 + -2x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 2x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 2x + 2x2)' equal to zero and attempt to solve: Simplifying 5 + 2x + 2x2 = 0 Solving 5 + 2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x + x2 = 0 + -2.5 x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 x + x2 = -2.5 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. + 0.25 + x2 = -2.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -2.5 + 0.25 Combine like terms: -2.5 + 0.25 = -2.25 1.25 + x2 = -2.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -2.25 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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