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Simplifying 4 + 13x(2 + -3x) = 39x + -2(13 + 2) 4 + (2 * 13x + -3x * 13x) = 39x + -2(13 + 2) 4 + (26x + -39x2) = 39x + -2(13 + 2) Combine like terms: 13 + 2 = 15 4 + 26x + -39x2 = 39x + -2(15) Multiply -2 * 15 4 + 26x + -39x2 = 39x + -30 Reorder the terms: 4 + 26x + -39x2 = -30 + 39x Solving 4 + 26x + -39x2 = -30 + 39x Solving for variable 'x'. Reorder the terms: 4 + 30 + 26x + -39x + -39x2 = -30 + 39x + 30 + -39x Combine like terms: 4 + 30 = 34 34 + 26x + -39x + -39x2 = -30 + 39x + 30 + -39x Combine like terms: 26x + -39x = -13x 34 + -13x + -39x2 = -30 + 39x + 30 + -39x Reorder the terms: 34 + -13x + -39x2 = -30 + 30 + 39x + -39x Combine like terms: -30 + 30 = 0 34 + -13x + -39x2 = 0 + 39x + -39x 34 + -13x + -39x2 = 39x + -39x Combine like terms: 39x + -39x = 0 34 + -13x + -39x2 = 0 Begin completing the square. Divide all terms by -39 the coefficient of the squared term: Divide each side by '-39'. -0.8717948718 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '0.8717948718' to each side of the equation. -0.8717948718 + 0.3333333333x + 0.8717948718 + x2 = 0 + 0.8717948718 Reorder the terms: -0.8717948718 + 0.8717948718 + 0.3333333333x + x2 = 0 + 0.8717948718 Combine like terms: -0.8717948718 + 0.8717948718 = 0.0000000000 0.0000000000 + 0.3333333333x + x2 = 0 + 0.8717948718 0.3333333333x + x2 = 0 + 0.8717948718 Combine like terms: 0 + 0.8717948718 = 0.8717948718 0.3333333333x + x2 = 0.8717948718 The x term is 0.3333333333x. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333x + 0.02777777779 + x2 = 0.8717948718 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = 0.8717948718 + 0.02777777779 Combine like terms: 0.8717948718 + 0.02777777779 = 0.89957264959 0.02777777779 + 0.3333333333x + x2 = 0.89957264959 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 0.89957264959 Calculate the square root of the right side: 0.948458038 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 0.948458038 and -0.948458038.Subproblem 1
x + 0.1666666667 = 0.948458038 Simplifying x + 0.1666666667 = 0.948458038 Reorder the terms: 0.1666666667 + x = 0.948458038 Solving 0.1666666667 + x = 0.948458038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = 0.948458038 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 0.948458038 + -0.1666666667 x = 0.948458038 + -0.1666666667 Combine like terms: 0.948458038 + -0.1666666667 = 0.7817913713 x = 0.7817913713 Simplifying x = 0.7817913713Subproblem 2
x + 0.1666666667 = -0.948458038 Simplifying x + 0.1666666667 = -0.948458038 Reorder the terms: 0.1666666667 + x = -0.948458038 Solving 0.1666666667 + x = -0.948458038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = -0.948458038 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -0.948458038 + -0.1666666667 x = -0.948458038 + -0.1666666667 Combine like terms: -0.948458038 + -0.1666666667 = -1.1151247047 x = -1.1151247047 Simplifying x = -1.1151247047Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7817913713, -1.1151247047}
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