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Simplifying (3x + -5)(3x + -5) = 11 Reorder the terms: (-5 + 3x)(3x + -5) = 11 Reorder the terms: (-5 + 3x)(-5 + 3x) = 11 Multiply (-5 + 3x) * (-5 + 3x) (-5(-5 + 3x) + 3x * (-5 + 3x)) = 11 ((-5 * -5 + 3x * -5) + 3x * (-5 + 3x)) = 11 ((25 + -15x) + 3x * (-5 + 3x)) = 11 (25 + -15x + (-5 * 3x + 3x * 3x)) = 11 (25 + -15x + (-15x + 9x2)) = 11 Combine like terms: -15x + -15x = -30x (25 + -30x + 9x2) = 11 Solving 25 + -30x + 9x2 = 11 Solving for variable 'x'. Reorder the terms: 25 + -11 + -30x + 9x2 = 11 + -11 Combine like terms: 25 + -11 = 14 14 + -30x + 9x2 = 11 + -11 Combine like terms: 11 + -11 = 0 14 + -30x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 1.555555556 + -3.333333333x + x2 = 0 Move the constant term to the right: Add '-1.555555556' to each side of the equation. 1.555555556 + -3.333333333x + -1.555555556 + x2 = 0 + -1.555555556 Reorder the terms: 1.555555556 + -1.555555556 + -3.333333333x + x2 = 0 + -1.555555556 Combine like terms: 1.555555556 + -1.555555556 = 0.000000000 0.000000000 + -3.333333333x + x2 = 0 + -1.555555556 -3.333333333x + x2 = 0 + -1.555555556 Combine like terms: 0 + -1.555555556 = -1.555555556 -3.333333333x + x2 = -1.555555556 The x term is -3.333333333x. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333x + 2.777777779 + x2 = -1.555555556 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333x + x2 = -1.555555556 + 2.777777779 Combine like terms: -1.555555556 + 2.777777779 = 1.222222223 2.777777779 + -3.333333333x + x2 = 1.222222223 Factor a perfect square on the left side: (x + -1.666666667)(x + -1.666666667) = 1.222222223 Calculate the square root of the right side: 1.105541597 Break this problem into two subproblems by setting (x + -1.666666667) equal to 1.105541597 and -1.105541597.Subproblem 1
x + -1.666666667 = 1.105541597 Simplifying x + -1.666666667 = 1.105541597 Reorder the terms: -1.666666667 + x = 1.105541597 Solving -1.666666667 + x = 1.105541597 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = 1.105541597 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = 1.105541597 + 1.666666667 x = 1.105541597 + 1.666666667 Combine like terms: 1.105541597 + 1.666666667 = 2.772208264 x = 2.772208264 Simplifying x = 2.772208264Subproblem 2
x + -1.666666667 = -1.105541597 Simplifying x + -1.666666667 = -1.105541597 Reorder the terms: -1.666666667 + x = -1.105541597 Solving -1.666666667 + x = -1.105541597 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = -1.105541597 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = -1.105541597 + 1.666666667 x = -1.105541597 + 1.666666667 Combine like terms: -1.105541597 + 1.666666667 = 0.56112507 x = 0.56112507 Simplifying x = 0.56112507Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.772208264, 0.56112507}
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