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Simplifying (5x2 + -7x + 3) + -1(8x2 + 2x + 11) = 0 Reorder the terms: (3 + -7x + 5x2) + -1(8x2 + 2x + 11) = 0 Remove parenthesis around (3 + -7x + 5x2) 3 + -7x + 5x2 + -1(8x2 + 2x + 11) = 0 Reorder the terms: 3 + -7x + 5x2 + -1(11 + 2x + 8x2) = 0 3 + -7x + 5x2 + (11 * -1 + 2x * -1 + 8x2 * -1) = 0 3 + -7x + 5x2 + (-11 + -2x + -8x2) = 0 Reorder the terms: 3 + -11 + -7x + -2x + 5x2 + -8x2 = 0 Combine like terms: 3 + -11 = -8 -8 + -7x + -2x + 5x2 + -8x2 = 0 Combine like terms: -7x + -2x = -9x -8 + -9x + 5x2 + -8x2 = 0 Combine like terms: 5x2 + -8x2 = -3x2 -8 + -9x + -3x2 = 0 Solving -8 + -9x + -3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + 9x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + 9x + 3x2)' equal to zero and attempt to solve: Simplifying 8 + 9x + 3x2 = 0 Solving 8 + 9x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.666666667 + 3x + x2 = 0 Move the constant term to the right: Add '-2.666666667' to each side of the equation. 2.666666667 + 3x + -2.666666667 + x2 = 0 + -2.666666667 Reorder the terms: 2.666666667 + -2.666666667 + 3x + x2 = 0 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + 3x + x2 = 0 + -2.666666667 3x + x2 = 0 + -2.666666667 Combine like terms: 0 + -2.666666667 = -2.666666667 3x + x2 = -2.666666667 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = -2.666666667 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -2.666666667 + 2.25 Combine like terms: -2.666666667 + 2.25 = -0.416666667 2.25 + 3x + x2 = -0.416666667 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = -0.416666667 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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