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Simplifying (-7x2) + -32x + -60 = 0 Reorder the terms: -60 + -32x + (-7x2) = 0 Solving -60 + -32x + (-7x2) = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(60 + 32x + (7x2)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(60 + 32x + (7x2))' equal to zero and attempt to solve: Simplifying 60 + 32x + (7x2) = 0 Solving 60 + 32x + (7x2) = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 8.571428571 + 4.571428571x + x2 = 0 Move the constant term to the right: Add '-8.571428571' to each side of the equation. 8.571428571 + 4.571428571x + -8.571428571 + x2 = 0 + -8.571428571 Reorder the terms: 8.571428571 + -8.571428571 + 4.571428571x + x2 = 0 + -8.571428571 Combine like terms: 8.571428571 + -8.571428571 = 0.000000000 0.000000000 + 4.571428571x + x2 = 0 + -8.571428571 4.571428571x + x2 = 0 + -8.571428571 Combine like terms: 0 + -8.571428571 = -8.571428571 4.571428571x + x2 = -8.571428571 The x term is 4.571428571x. Take half its coefficient (2.285714286). Square it (5.224489797) and add it to both sides. Add '5.224489797' to each side of the equation. 4.571428571x + 5.224489797 + x2 = -8.571428571 + 5.224489797 Reorder the terms: 5.224489797 + 4.571428571x + x2 = -8.571428571 + 5.224489797 Combine like terms: -8.571428571 + 5.224489797 = -3.346938774 5.224489797 + 4.571428571x + x2 = -3.346938774 Factor a perfect square on the left side: ((x) + 2.285714286)((x) + 2.285714286) = -3.346938774 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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