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Simplifying -12x(x + -5) + 7x(3 + -1x) = 5 Reorder the terms: -12x(-5 + x) + 7x(3 + -1x) = 5 (-5 * -12x + x * -12x) + 7x(3 + -1x) = 5 (60x + -12x2) + 7x(3 + -1x) = 5 60x + -12x2 + (3 * 7x + -1x * 7x) = 5 60x + -12x2 + (21x + -7x2) = 5 Reorder the terms: 60x + 21x + -12x2 + -7x2 = 5 Combine like terms: 60x + 21x = 81x 81x + -12x2 + -7x2 = 5 Combine like terms: -12x2 + -7x2 = -19x2 81x + -19x2 = 5 Solving 81x + -19x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 81x + -19x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 81x + -19x2 = 0 Begin completing the square. Divide all terms by -19 the coefficient of the squared term: Divide each side by '-19'. 0.2631578947 + -4.263157895x + x2 = 0 Move the constant term to the right: Add '-0.2631578947' to each side of the equation. 0.2631578947 + -4.263157895x + -0.2631578947 + x2 = 0 + -0.2631578947 Reorder the terms: 0.2631578947 + -0.2631578947 + -4.263157895x + x2 = 0 + -0.2631578947 Combine like terms: 0.2631578947 + -0.2631578947 = 0.0000000000 0.0000000000 + -4.263157895x + x2 = 0 + -0.2631578947 -4.263157895x + x2 = 0 + -0.2631578947 Combine like terms: 0 + -0.2631578947 = -0.2631578947 -4.263157895x + x2 = -0.2631578947 The x term is -4.263157895x. Take half its coefficient (-2.131578948). Square it (4.543628812) and add it to both sides. Add '4.543628812' to each side of the equation. -4.263157895x + 4.543628812 + x2 = -0.2631578947 + 4.543628812 Reorder the terms: 4.543628812 + -4.263157895x + x2 = -0.2631578947 + 4.543628812 Combine like terms: -0.2631578947 + 4.543628812 = 4.2804709173 4.543628812 + -4.263157895x + x2 = 4.2804709173 Factor a perfect square on the left side: (x + -2.131578948)(x + -2.131578948) = 4.2804709173 Calculate the square root of the right side: 2.068929897 Break this problem into two subproblems by setting (x + -2.131578948) equal to 2.068929897 and -2.068929897.Subproblem 1
x + -2.131578948 = 2.068929897 Simplifying x + -2.131578948 = 2.068929897 Reorder the terms: -2.131578948 + x = 2.068929897 Solving -2.131578948 + x = 2.068929897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.131578948' to each side of the equation. -2.131578948 + 2.131578948 + x = 2.068929897 + 2.131578948 Combine like terms: -2.131578948 + 2.131578948 = 0.000000000 0.000000000 + x = 2.068929897 + 2.131578948 x = 2.068929897 + 2.131578948 Combine like terms: 2.068929897 + 2.131578948 = 4.200508845 x = 4.200508845 Simplifying x = 4.200508845Subproblem 2
x + -2.131578948 = -2.068929897 Simplifying x + -2.131578948 = -2.068929897 Reorder the terms: -2.131578948 + x = -2.068929897 Solving -2.131578948 + x = -2.068929897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.131578948' to each side of the equation. -2.131578948 + 2.131578948 + x = -2.068929897 + 2.131578948 Combine like terms: -2.131578948 + 2.131578948 = 0.000000000 0.000000000 + x = -2.068929897 + 2.131578948 x = -2.068929897 + 2.131578948 Combine like terms: -2.068929897 + 2.131578948 = 0.062649051 x = 0.062649051 Simplifying x = 0.062649051Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.200508845, 0.062649051}
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