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Simplifying 60x2 + 71x + 57 = 3 + 7x Reorder the terms: 57 + 71x + 60x2 = 3 + 7x Solving 57 + 71x + 60x2 = 3 + 7x Solving for variable 'x'. Reorder the terms: 57 + -3 + 71x + -7x + 60x2 = 3 + 7x + -3 + -7x Combine like terms: 57 + -3 = 54 54 + 71x + -7x + 60x2 = 3 + 7x + -3 + -7x Combine like terms: 71x + -7x = 64x 54 + 64x + 60x2 = 3 + 7x + -3 + -7x Reorder the terms: 54 + 64x + 60x2 = 3 + -3 + 7x + -7x Combine like terms: 3 + -3 = 0 54 + 64x + 60x2 = 0 + 7x + -7x 54 + 64x + 60x2 = 7x + -7x Combine like terms: 7x + -7x = 0 54 + 64x + 60x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(27 + 32x + 30x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(27 + 32x + 30x2)' equal to zero and attempt to solve: Simplifying 27 + 32x + 30x2 = 0 Solving 27 + 32x + 30x2 = 0 Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. 0.9 + 1.066666667x + x2 = 0.0 Move the constant term to the right: Add '-0.9' to each side of the equation. 0.9 + 1.066666667x + -0.9 + x2 = 0.0 + -0.9 Reorder the terms: 0.9 + -0.9 + 1.066666667x + x2 = 0.0 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + 1.066666667x + x2 = 0.0 + -0.9 1.066666667x + x2 = 0.0 + -0.9 Combine like terms: 0.0 + -0.9 = -0.9 1.066666667x + x2 = -0.9 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 = -0.9 + 0.2844444446 Reorder the terms: 0.2844444446 + 1.066666667x + x2 = -0.9 + 0.2844444446 Combine like terms: -0.9 + 0.2844444446 = -0.6155555554 0.2844444446 + 1.066666667x + x2 = -0.6155555554 Factor a perfect square on the left side: (x + 0.5333333335)(x + 0.5333333335) = -0.6155555554 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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