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Simplifying (14x2 + 6x + 10) + -1(2x2 + 8) = 0 Reorder the terms: (10 + 6x + 14x2) + -1(2x2 + 8) = 0 Remove parenthesis around (10 + 6x + 14x2) 10 + 6x + 14x2 + -1(2x2 + 8) = 0 Reorder the terms: 10 + 6x + 14x2 + -1(8 + 2x2) = 0 10 + 6x + 14x2 + (8 * -1 + 2x2 * -1) = 0 10 + 6x + 14x2 + (-8 + -2x2) = 0 Reorder the terms: 10 + -8 + 6x + 14x2 + -2x2 = 0 Combine like terms: 10 + -8 = 2 2 + 6x + 14x2 + -2x2 = 0 Combine like terms: 14x2 + -2x2 = 12x2 2 + 6x + 12x2 = 0 Solving 2 + 6x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 3x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 3x + 6x2)' equal to zero and attempt to solve: Simplifying 1 + 3x + 6x2 = 0 Solving 1 + 3x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.1666666667 + 0.5x + x2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + 0.5x + -0.1666666667 + x2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + 0.5x + x2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + 0.5x + x2 = 0 + -0.1666666667 0.5x + x2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 0.5x + x2 = -0.1666666667 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = -0.1666666667 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = -0.1666666667 + 0.0625 Combine like terms: -0.1666666667 + 0.0625 = -0.1041666667 0.0625 + 0.5x + x2 = -0.1041666667 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = -0.1041666667 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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