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Simplifying -7m2 + -32m + 24 = 0 Reorder the terms: 24 + -32m + -7m2 = 0 Solving 24 + -32m + -7m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -3.428571429 + 4.571428571m + m2 = 0 Move the constant term to the right: Add '3.428571429' to each side of the equation. -3.428571429 + 4.571428571m + 3.428571429 + m2 = 0 + 3.428571429 Reorder the terms: -3.428571429 + 3.428571429 + 4.571428571m + m2 = 0 + 3.428571429 Combine like terms: -3.428571429 + 3.428571429 = 0.000000000 0.000000000 + 4.571428571m + m2 = 0 + 3.428571429 4.571428571m + m2 = 0 + 3.428571429 Combine like terms: 0 + 3.428571429 = 3.428571429 4.571428571m + m2 = 3.428571429 The m term is 4.571428571m. Take half its coefficient (2.285714286). Square it (5.224489797) and add it to both sides. Add '5.224489797' to each side of the equation. 4.571428571m + 5.224489797 + m2 = 3.428571429 + 5.224489797 Reorder the terms: 5.224489797 + 4.571428571m + m2 = 3.428571429 + 5.224489797 Combine like terms: 3.428571429 + 5.224489797 = 8.653061226 5.224489797 + 4.571428571m + m2 = 8.653061226 Factor a perfect square on the left side: (m + 2.285714286)(m + 2.285714286) = 8.653061226 Calculate the square root of the right side: 2.941608612 Break this problem into two subproblems by setting (m + 2.285714286) equal to 2.941608612 and -2.941608612.Subproblem 1
m + 2.285714286 = 2.941608612 Simplifying m + 2.285714286 = 2.941608612 Reorder the terms: 2.285714286 + m = 2.941608612 Solving 2.285714286 + m = 2.941608612 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2.285714286' to each side of the equation. 2.285714286 + -2.285714286 + m = 2.941608612 + -2.285714286 Combine like terms: 2.285714286 + -2.285714286 = 0.000000000 0.000000000 + m = 2.941608612 + -2.285714286 m = 2.941608612 + -2.285714286 Combine like terms: 2.941608612 + -2.285714286 = 0.655894326 m = 0.655894326 Simplifying m = 0.655894326Subproblem 2
m + 2.285714286 = -2.941608612 Simplifying m + 2.285714286 = -2.941608612 Reorder the terms: 2.285714286 + m = -2.941608612 Solving 2.285714286 + m = -2.941608612 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2.285714286' to each side of the equation. 2.285714286 + -2.285714286 + m = -2.941608612 + -2.285714286 Combine like terms: 2.285714286 + -2.285714286 = 0.000000000 0.000000000 + m = -2.941608612 + -2.285714286 m = -2.941608612 + -2.285714286 Combine like terms: -2.941608612 + -2.285714286 = -5.227322898 m = -5.227322898 Simplifying m = -5.227322898Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.655894326, -5.227322898}
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