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Simplifying 3 + -10x(6 + -5x) = 7x + -16 + 3x 3 + (6 * -10x + -5x * -10x) = 7x + -16 + 3x 3 + (-60x + 50x2) = 7x + -16 + 3x Reorder the terms: 3 + -60x + 50x2 = -16 + 7x + 3x Combine like terms: 7x + 3x = 10x 3 + -60x + 50x2 = -16 + 10x Solving 3 + -60x + 50x2 = -16 + 10x Solving for variable 'x'. Reorder the terms: 3 + 16 + -60x + -10x + 50x2 = -16 + 10x + 16 + -10x Combine like terms: 3 + 16 = 19 19 + -60x + -10x + 50x2 = -16 + 10x + 16 + -10x Combine like terms: -60x + -10x = -70x 19 + -70x + 50x2 = -16 + 10x + 16 + -10x Reorder the terms: 19 + -70x + 50x2 = -16 + 16 + 10x + -10x Combine like terms: -16 + 16 = 0 19 + -70x + 50x2 = 0 + 10x + -10x 19 + -70x + 50x2 = 10x + -10x Combine like terms: 10x + -10x = 0 19 + -70x + 50x2 = 0 Begin completing the square. Divide all terms by 50 the coefficient of the squared term: Divide each side by '50'. 0.38 + -1.4x + x2 = 0 Move the constant term to the right: Add '-0.38' to each side of the equation. 0.38 + -1.4x + -0.38 + x2 = 0 + -0.38 Reorder the terms: 0.38 + -0.38 + -1.4x + x2 = 0 + -0.38 Combine like terms: 0.38 + -0.38 = 0.00 0.00 + -1.4x + x2 = 0 + -0.38 -1.4x + x2 = 0 + -0.38 Combine like terms: 0 + -0.38 = -0.38 -1.4x + x2 = -0.38 The x term is -1.4x. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4x + 0.49 + x2 = -0.38 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = -0.38 + 0.49 Combine like terms: -0.38 + 0.49 = 0.11 0.49 + -1.4x + x2 = 0.11 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = 0.11 Calculate the square root of the right side: 0.331662479 Break this problem into two subproblems by setting (x + -0.7) equal to 0.331662479 and -0.331662479.Subproblem 1
x + -0.7 = 0.331662479 Simplifying x + -0.7 = 0.331662479 Reorder the terms: -0.7 + x = 0.331662479 Solving -0.7 + x = 0.331662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = 0.331662479 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 0.331662479 + 0.7 x = 0.331662479 + 0.7 Combine like terms: 0.331662479 + 0.7 = 1.031662479 x = 1.031662479 Simplifying x = 1.031662479Subproblem 2
x + -0.7 = -0.331662479 Simplifying x + -0.7 = -0.331662479 Reorder the terms: -0.7 + x = -0.331662479 Solving -0.7 + x = -0.331662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = -0.331662479 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -0.331662479 + 0.7 x = -0.331662479 + 0.7 Combine like terms: -0.331662479 + 0.7 = 0.368337521 x = 0.368337521 Simplifying x = 0.368337521Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.031662479, 0.368337521}
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