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Simplifying -4x2 + -1(3x2 + 8x + -3) + -1(5x2 + -3x + 5) = 0 Reorder the terms: -4x2 + -1(-3 + 8x + 3x2) + -1(5x2 + -3x + 5) = 0 -4x2 + (-3 * -1 + 8x * -1 + 3x2 * -1) + -1(5x2 + -3x + 5) = 0 -4x2 + (3 + -8x + -3x2) + -1(5x2 + -3x + 5) = 0 Reorder the terms: -4x2 + 3 + -8x + -3x2 + -1(5 + -3x + 5x2) = 0 -4x2 + 3 + -8x + -3x2 + (5 * -1 + -3x * -1 + 5x2 * -1) = 0 -4x2 + 3 + -8x + -3x2 + (-5 + 3x + -5x2) = 0 Reorder the terms: 3 + -5 + -8x + 3x + -4x2 + -3x2 + -5x2 = 0 Combine like terms: 3 + -5 = -2 -2 + -8x + 3x + -4x2 + -3x2 + -5x2 = 0 Combine like terms: -8x + 3x = -5x -2 + -5x + -4x2 + -3x2 + -5x2 = 0 Combine like terms: -4x2 + -3x2 = -7x2 -2 + -5x + -7x2 + -5x2 = 0 Combine like terms: -7x2 + -5x2 = -12x2 -2 + -5x + -12x2 = 0 Solving -2 + -5x + -12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + 5x + 12x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + 5x + 12x2)' equal to zero and attempt to solve: Simplifying 2 + 5x + 12x2 = 0 Solving 2 + 5x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.1666666667 + 0.4166666667x + x2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + 0.4166666667x + -0.1666666667 + x2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + 0.4166666667x + x2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + 0.4166666667x + x2 = 0 + -0.1666666667 0.4166666667x + x2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 0.4166666667x + x2 = -0.1666666667 The x term is 0.4166666667x. Take half its coefficient (0.2083333334). Square it (0.04340277781) and add it to both sides. Add '0.04340277781' to each side of the equation. 0.4166666667x + 0.04340277781 + x2 = -0.1666666667 + 0.04340277781 Reorder the terms: 0.04340277781 + 0.4166666667x + x2 = -0.1666666667 + 0.04340277781 Combine like terms: -0.1666666667 + 0.04340277781 = -0.12326388889 0.04340277781 + 0.4166666667x + x2 = -0.12326388889 Factor a perfect square on the left side: (x + 0.2083333334)(x + 0.2083333334) = -0.12326388889 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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