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Simplifying (3x + -11)(3x + -11) = 5 Reorder the terms: (-11 + 3x)(3x + -11) = 5 Reorder the terms: (-11 + 3x)(-11 + 3x) = 5 Multiply (-11 + 3x) * (-11 + 3x) (-11(-11 + 3x) + 3x * (-11 + 3x)) = 5 ((-11 * -11 + 3x * -11) + 3x * (-11 + 3x)) = 5 ((121 + -33x) + 3x * (-11 + 3x)) = 5 (121 + -33x + (-11 * 3x + 3x * 3x)) = 5 (121 + -33x + (-33x + 9x2)) = 5 Combine like terms: -33x + -33x = -66x (121 + -66x + 9x2) = 5 Solving 121 + -66x + 9x2 = 5 Solving for variable 'x'. Reorder the terms: 121 + -5 + -66x + 9x2 = 5 + -5 Combine like terms: 121 + -5 = 116 116 + -66x + 9x2 = 5 + -5 Combine like terms: 5 + -5 = 0 116 + -66x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 12.88888889 + -7.333333333x + x2 = 0 Move the constant term to the right: Add '-12.88888889' to each side of the equation. 12.88888889 + -7.333333333x + -12.88888889 + x2 = 0 + -12.88888889 Reorder the terms: 12.88888889 + -12.88888889 + -7.333333333x + x2 = 0 + -12.88888889 Combine like terms: 12.88888889 + -12.88888889 = 0.00000000 0.00000000 + -7.333333333x + x2 = 0 + -12.88888889 -7.333333333x + x2 = 0 + -12.88888889 Combine like terms: 0 + -12.88888889 = -12.88888889 -7.333333333x + x2 = -12.88888889 The x term is -7.333333333x. Take half its coefficient (-3.666666667). Square it (13.44444445) and add it to both sides. Add '13.44444445' to each side of the equation. -7.333333333x + 13.44444445 + x2 = -12.88888889 + 13.44444445 Reorder the terms: 13.44444445 + -7.333333333x + x2 = -12.88888889 + 13.44444445 Combine like terms: -12.88888889 + 13.44444445 = 0.55555556 13.44444445 + -7.333333333x + x2 = 0.55555556 Factor a perfect square on the left side: (x + -3.666666667)(x + -3.666666667) = 0.55555556 Calculate the square root of the right side: 0.745355995 Break this problem into two subproblems by setting (x + -3.666666667) equal to 0.745355995 and -0.745355995.Subproblem 1
x + -3.666666667 = 0.745355995 Simplifying x + -3.666666667 = 0.745355995 Reorder the terms: -3.666666667 + x = 0.745355995 Solving -3.666666667 + x = 0.745355995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.666666667' to each side of the equation. -3.666666667 + 3.666666667 + x = 0.745355995 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + x = 0.745355995 + 3.666666667 x = 0.745355995 + 3.666666667 Combine like terms: 0.745355995 + 3.666666667 = 4.412022662 x = 4.412022662 Simplifying x = 4.412022662Subproblem 2
x + -3.666666667 = -0.745355995 Simplifying x + -3.666666667 = -0.745355995 Reorder the terms: -3.666666667 + x = -0.745355995 Solving -3.666666667 + x = -0.745355995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.666666667' to each side of the equation. -3.666666667 + 3.666666667 + x = -0.745355995 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + x = -0.745355995 + 3.666666667 x = -0.745355995 + 3.666666667 Combine like terms: -0.745355995 + 3.666666667 = 2.921310672 x = 2.921310672 Simplifying x = 2.921310672Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.412022662, 2.921310672}
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