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Simplifying -3x2 + -7x = 11 Reorder the terms: -7x + -3x2 = 11 Solving -7x + -3x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + -7x + -3x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + -7x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(11 + 7x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(11 + 7x + 3x2)' equal to zero and attempt to solve: Simplifying 11 + 7x + 3x2 = 0 Solving 11 + 7x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3.666666667 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '-3.666666667' to each side of the equation. 3.666666667 + 2.333333333x + -3.666666667 + x2 = 0 + -3.666666667 Reorder the terms: 3.666666667 + -3.666666667 + 2.333333333x + x2 = 0 + -3.666666667 Combine like terms: 3.666666667 + -3.666666667 = 0.000000000 0.000000000 + 2.333333333x + x2 = 0 + -3.666666667 2.333333333x + x2 = 0 + -3.666666667 Combine like terms: 0 + -3.666666667 = -3.666666667 2.333333333x + x2 = -3.666666667 The x term is 2.333333333x. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333x + 1.361111112 + x2 = -3.666666667 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = -3.666666667 + 1.361111112 Combine like terms: -3.666666667 + 1.361111112 = -2.305555555 1.361111112 + 2.333333333x + x2 = -2.305555555 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = -2.305555555 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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