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Simplifying (3x + -5)(3x + -5) = 48 Reorder the terms: (-5 + 3x)(3x + -5) = 48 Reorder the terms: (-5 + 3x)(-5 + 3x) = 48 Multiply (-5 + 3x) * (-5 + 3x) (-5(-5 + 3x) + 3x * (-5 + 3x)) = 48 ((-5 * -5 + 3x * -5) + 3x * (-5 + 3x)) = 48 ((25 + -15x) + 3x * (-5 + 3x)) = 48 (25 + -15x + (-5 * 3x + 3x * 3x)) = 48 (25 + -15x + (-15x + 9x2)) = 48 Combine like terms: -15x + -15x = -30x (25 + -30x + 9x2) = 48 Solving 25 + -30x + 9x2 = 48 Solving for variable 'x'. Reorder the terms: 25 + -48 + -30x + 9x2 = 48 + -48 Combine like terms: 25 + -48 = -23 -23 + -30x + 9x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -23 + -30x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.555555556 + -3.333333333x + x2 = 0 Move the constant term to the right: Add '2.555555556' to each side of the equation. -2.555555556 + -3.333333333x + 2.555555556 + x2 = 0 + 2.555555556 Reorder the terms: -2.555555556 + 2.555555556 + -3.333333333x + x2 = 0 + 2.555555556 Combine like terms: -2.555555556 + 2.555555556 = 0.000000000 0.000000000 + -3.333333333x + x2 = 0 + 2.555555556 -3.333333333x + x2 = 0 + 2.555555556 Combine like terms: 0 + 2.555555556 = 2.555555556 -3.333333333x + x2 = 2.555555556 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 = 2.555555556 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333x + x2 = 2.555555556 + 2.777777779 Combine like terms: 2.555555556 + 2.777777779 = 5.333333335 2.777777779 + -3.333333333x + x2 = 5.333333335 Factor a perfect square on the left side: (x + -1.666666667)(x + -1.666666667) = 5.333333335 Calculate the square root of the right side: 2.309401077 Break this problem into two subproblems by setting (x + -1.666666667) equal to 2.309401077 and -2.309401077.Subproblem 1
x + -1.666666667 = 2.309401077 Simplifying x + -1.666666667 = 2.309401077 Reorder the terms: -1.666666667 + x = 2.309401077 Solving -1.666666667 + x = 2.309401077 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 = 2.309401077 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = 2.309401077 + 1.666666667 x = 2.309401077 + 1.666666667 Combine like terms: 2.309401077 + 1.666666667 = 3.976067744 x = 3.976067744 Simplifying x = 3.976067744Subproblem 2
x + -1.666666667 = -2.309401077 Simplifying x + -1.666666667 = -2.309401077 Reorder the terms: -1.666666667 + x = -2.309401077 Solving -1.666666667 + x = -2.309401077 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 = -2.309401077 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = -2.309401077 + 1.666666667 x = -2.309401077 + 1.666666667 Combine like terms: -2.309401077 + 1.666666667 = -0.64273441 x = -0.64273441 Simplifying x = -0.64273441Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.976067744, -0.64273441}
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