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Simplifying -7x2 + -6x = 68 Reorder the terms: -6x + -7x2 = 68 Solving -6x + -7x2 = 68 Solving for variable 'x'. Reorder the terms: -68 + -6x + -7x2 = 68 + -68 Combine like terms: 68 + -68 = 0 -68 + -6x + -7x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(68 + 6x + 7x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(68 + 6x + 7x2)' equal to zero and attempt to solve: Simplifying 68 + 6x + 7x2 = 0 Solving 68 + 6x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 9.714285714 + 0.8571428571x + x2 = 0 Move the constant term to the right: Add '-9.714285714' to each side of the equation. 9.714285714 + 0.8571428571x + -9.714285714 + x2 = 0 + -9.714285714 Reorder the terms: 9.714285714 + -9.714285714 + 0.8571428571x + x2 = 0 + -9.714285714 Combine like terms: 9.714285714 + -9.714285714 = 0.000000000 0.000000000 + 0.8571428571x + x2 = 0 + -9.714285714 0.8571428571x + x2 = 0 + -9.714285714 Combine like terms: 0 + -9.714285714 = -9.714285714 0.8571428571x + x2 = -9.714285714 The x term is 0.8571428571x. Take half its coefficient (0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. 0.8571428571x + 0.1836734694 + x2 = -9.714285714 + 0.1836734694 Reorder the terms: 0.1836734694 + 0.8571428571x + x2 = -9.714285714 + 0.1836734694 Combine like terms: -9.714285714 + 0.1836734694 = -9.5306122446 0.1836734694 + 0.8571428571x + x2 = -9.5306122446 Factor a perfect square on the left side: (x + 0.4285714286)(x + 0.4285714286) = -9.5306122446 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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