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Simplifying 47m2 + 88m + 39 = 0 Reorder the terms: 39 + 88m + 47m2 = 0 Solving 39 + 88m + 47m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 47 the coefficient of the squared term: Divide each side by '47'. 0.829787234 + 1.872340426m + m2 = 0 Move the constant term to the right: Add '-0.829787234' to each side of the equation. 0.829787234 + 1.872340426m + -0.829787234 + m2 = 0 + -0.829787234 Reorder the terms: 0.829787234 + -0.829787234 + 1.872340426m + m2 = 0 + -0.829787234 Combine like terms: 0.829787234 + -0.829787234 = 0.000000000 0.000000000 + 1.872340426m + m2 = 0 + -0.829787234 1.872340426m + m2 = 0 + -0.829787234 Combine like terms: 0 + -0.829787234 = -0.829787234 1.872340426m + m2 = -0.829787234 The m term is 1.872340426m. Take half its coefficient (0.936170213). Square it (0.8764146677) and add it to both sides. Add '0.8764146677' to each side of the equation. 1.872340426m + 0.8764146677 + m2 = -0.829787234 + 0.8764146677 Reorder the terms: 0.8764146677 + 1.872340426m + m2 = -0.829787234 + 0.8764146677 Combine like terms: -0.829787234 + 0.8764146677 = 0.0466274337 0.8764146677 + 1.872340426m + m2 = 0.0466274337 Factor a perfect square on the left side: (m + 0.936170213)(m + 0.936170213) = 0.0466274337 Calculate the square root of the right side: 0.215933864 Break this problem into two subproblems by setting (m + 0.936170213) equal to 0.215933864 and -0.215933864.Subproblem 1
m + 0.936170213 = 0.215933864 Simplifying m + 0.936170213 = 0.215933864 Reorder the terms: 0.936170213 + m = 0.215933864 Solving 0.936170213 + m = 0.215933864 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.936170213' to each side of the equation. 0.936170213 + -0.936170213 + m = 0.215933864 + -0.936170213 Combine like terms: 0.936170213 + -0.936170213 = 0.000000000 0.000000000 + m = 0.215933864 + -0.936170213 m = 0.215933864 + -0.936170213 Combine like terms: 0.215933864 + -0.936170213 = -0.720236349 m = -0.720236349 Simplifying m = -0.720236349Subproblem 2
m + 0.936170213 = -0.215933864 Simplifying m + 0.936170213 = -0.215933864 Reorder the terms: 0.936170213 + m = -0.215933864 Solving 0.936170213 + m = -0.215933864 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.936170213' to each side of the equation. 0.936170213 + -0.936170213 + m = -0.215933864 + -0.936170213 Combine like terms: 0.936170213 + -0.936170213 = 0.000000000 0.000000000 + m = -0.215933864 + -0.936170213 m = -0.215933864 + -0.936170213 Combine like terms: -0.215933864 + -0.936170213 = -1.152104077 m = -1.152104077 Simplifying m = -1.152104077Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.720236349, -1.152104077}
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