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Simplifying 6x(5x + 5) = -8 + -2(x + 17) Reorder the terms: 6x(5 + 5x) = -8 + -2(x + 17) (5 * 6x + 5x * 6x) = -8 + -2(x + 17) (30x + 30x2) = -8 + -2(x + 17) Reorder the terms: 30x + 30x2 = -8 + -2(17 + x) 30x + 30x2 = -8 + (17 * -2 + x * -2) 30x + 30x2 = -8 + (-34 + -2x) Combine like terms: -8 + -34 = -42 30x + 30x2 = -42 + -2x Solving 30x + 30x2 = -42 + -2x Solving for variable 'x'. Reorder the terms: 42 + 30x + 2x + 30x2 = -42 + -2x + 42 + 2x Combine like terms: 30x + 2x = 32x 42 + 32x + 30x2 = -42 + -2x + 42 + 2x Reorder the terms: 42 + 32x + 30x2 = -42 + 42 + -2x + 2x Combine like terms: -42 + 42 = 0 42 + 32x + 30x2 = 0 + -2x + 2x 42 + 32x + 30x2 = -2x + 2x Combine like terms: -2x + 2x = 0 42 + 32x + 30x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(21 + 16x + 15x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(21 + 16x + 15x2)' equal to zero and attempt to solve: Simplifying 21 + 16x + 15x2 = 0 Solving 21 + 16x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 1.4 + 1.066666667x + x2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + 1.066666667x + -1.4 + x2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + 1.066666667x + x2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + 1.066666667x + x2 = 0 + -1.4 1.066666667x + x2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 1.066666667x + x2 = -1.4 The x term is 1.066666667x. Take half its coefficient (0.5333333335). Square it (0.2844444446) and add it to both sides. Add '0.2844444446' to each side of the equation. 1.066666667x + 0.2844444446 + x2 = -1.4 + 0.2844444446 Reorder the terms: 0.2844444446 + 1.066666667x + x2 = -1.4 + 0.2844444446 Combine like terms: -1.4 + 0.2844444446 = -1.1155555554 0.2844444446 + 1.066666667x + x2 = -1.1155555554 Factor a perfect square on the left side: (x + 0.5333333335)(x + 0.5333333335) = -1.1155555554 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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