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Simplifying 9x2 + 22x + -49 + -13x2 + -8x + 15 = 0 Reorder the terms: -49 + 15 + 22x + -8x + 9x2 + -13x2 = 0 Combine like terms: -49 + 15 = -34 -34 + 22x + -8x + 9x2 + -13x2 = 0 Combine like terms: 22x + -8x = 14x -34 + 14x + 9x2 + -13x2 = 0 Combine like terms: 9x2 + -13x2 = -4x2 -34 + 14x + -4x2 = 0 Solving -34 + 14x + -4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-17 + 7x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-17 + 7x + -2x2)' equal to zero and attempt to solve: Simplifying -17 + 7x + -2x2 = 0 Solving -17 + 7x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 8.5 + -3.5x + x2 = 0 Move the constant term to the right: Add '-8.5' to each side of the equation. 8.5 + -3.5x + -8.5 + x2 = 0 + -8.5 Reorder the terms: 8.5 + -8.5 + -3.5x + x2 = 0 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + -3.5x + x2 = 0 + -8.5 -3.5x + x2 = 0 + -8.5 Combine like terms: 0 + -8.5 = -8.5 -3.5x + x2 = -8.5 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = -8.5 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = -8.5 + 3.0625 Combine like terms: -8.5 + 3.0625 = -5.4375 3.0625 + -3.5x + x2 = -5.4375 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = -5.4375 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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