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Simplifying 4 + 13x(2 + -3x) = 6x + -14(3x + 12) 4 + (2 * 13x + -3x * 13x) = 6x + -14(3x + 12) 4 + (26x + -39x2) = 6x + -14(3x + 12) Reorder the terms: 4 + 26x + -39x2 = 6x + -14(12 + 3x) 4 + 26x + -39x2 = 6x + (12 * -14 + 3x * -14) 4 + 26x + -39x2 = 6x + (-168 + -42x) Reorder the terms: 4 + 26x + -39x2 = -168 + 6x + -42x Combine like terms: 6x + -42x = -36x 4 + 26x + -39x2 = -168 + -36x Solving 4 + 26x + -39x2 = -168 + -36x Solving for variable 'x'. Reorder the terms: 4 + 168 + 26x + 36x + -39x2 = -168 + -36x + 168 + 36x Combine like terms: 4 + 168 = 172 172 + 26x + 36x + -39x2 = -168 + -36x + 168 + 36x Combine like terms: 26x + 36x = 62x 172 + 62x + -39x2 = -168 + -36x + 168 + 36x Reorder the terms: 172 + 62x + -39x2 = -168 + 168 + -36x + 36x Combine like terms: -168 + 168 = 0 172 + 62x + -39x2 = 0 + -36x + 36x 172 + 62x + -39x2 = -36x + 36x Combine like terms: -36x + 36x = 0 172 + 62x + -39x2 = 0 Begin completing the square. Divide all terms by -39 the coefficient of the squared term: Divide each side by '-39'. -4.41025641 + -1.58974359x + x2 = 0 Move the constant term to the right: Add '4.41025641' to each side of the equation. -4.41025641 + -1.58974359x + 4.41025641 + x2 = 0 + 4.41025641 Reorder the terms: -4.41025641 + 4.41025641 + -1.58974359x + x2 = 0 + 4.41025641 Combine like terms: -4.41025641 + 4.41025641 = 0.00000000 0.00000000 + -1.58974359x + x2 = 0 + 4.41025641 -1.58974359x + x2 = 0 + 4.41025641 Combine like terms: 0 + 4.41025641 = 4.41025641 -1.58974359x + x2 = 4.41025641 The x term is -1.58974359x. Take half its coefficient (-0.794871795). Square it (0.6318211705) and add it to both sides. Add '0.6318211705' to each side of the equation. -1.58974359x + 0.6318211705 + x2 = 4.41025641 + 0.6318211705 Reorder the terms: 0.6318211705 + -1.58974359x + x2 = 4.41025641 + 0.6318211705 Combine like terms: 4.41025641 + 0.6318211705 = 5.0420775805 0.6318211705 + -1.58974359x + x2 = 5.0420775805 Factor a perfect square on the left side: (x + -0.794871795)(x + -0.794871795) = 5.0420775805 Calculate the square root of the right side: 2.245457098 Break this problem into two subproblems by setting (x + -0.794871795) equal to 2.245457098 and -2.245457098.Subproblem 1
x + -0.794871795 = 2.245457098 Simplifying x + -0.794871795 = 2.245457098 Reorder the terms: -0.794871795 + x = 2.245457098 Solving -0.794871795 + x = 2.245457098 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.794871795' to each side of the equation. -0.794871795 + 0.794871795 + x = 2.245457098 + 0.794871795 Combine like terms: -0.794871795 + 0.794871795 = 0.000000000 0.000000000 + x = 2.245457098 + 0.794871795 x = 2.245457098 + 0.794871795 Combine like terms: 2.245457098 + 0.794871795 = 3.040328893 x = 3.040328893 Simplifying x = 3.040328893Subproblem 2
x + -0.794871795 = -2.245457098 Simplifying x + -0.794871795 = -2.245457098 Reorder the terms: -0.794871795 + x = -2.245457098 Solving -0.794871795 + x = -2.245457098 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.794871795' to each side of the equation. -0.794871795 + 0.794871795 + x = -2.245457098 + 0.794871795 Combine like terms: -0.794871795 + 0.794871795 = 0.000000000 0.000000000 + x = -2.245457098 + 0.794871795 x = -2.245457098 + 0.794871795 Combine like terms: -2.245457098 + 0.794871795 = -1.450585303 x = -1.450585303 Simplifying x = -1.450585303Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.040328893, -1.450585303}
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