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Simplifying (x2 + -7x + -6) + -1(9x2 + 3x + 2) = 0 Reorder the terms: (-6 + -7x + x2) + -1(9x2 + 3x + 2) = 0 Remove parenthesis around (-6 + -7x + x2) -6 + -7x + x2 + -1(9x2 + 3x + 2) = 0 Reorder the terms: -6 + -7x + x2 + -1(2 + 3x + 9x2) = 0 -6 + -7x + x2 + (2 * -1 + 3x * -1 + 9x2 * -1) = 0 -6 + -7x + x2 + (-2 + -3x + -9x2) = 0 Reorder the terms: -6 + -2 + -7x + -3x + x2 + -9x2 = 0 Combine like terms: -6 + -2 = -8 -8 + -7x + -3x + x2 + -9x2 = 0 Combine like terms: -7x + -3x = -10x -8 + -10x + x2 + -9x2 = 0 Combine like terms: x2 + -9x2 = -8x2 -8 + -10x + -8x2 = 0 Solving -8 + -10x + -8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-2'. -2(4 + 5x + 4x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(4 + 5x + 4x2)' equal to zero and attempt to solve: Simplifying 4 + 5x + 4x2 = 0 Solving 4 + 5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1 + 1.25x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 1.25x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 1.25x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 1.25x + x2 = 0 + -1 1.25x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 1.25x + x2 = -1 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = -1 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = -1 + 0.390625 Combine like terms: -1 + 0.390625 = -0.609375 0.390625 + 1.25x + x2 = -0.609375 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = -0.609375 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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