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Simplifying 2m2 + 9m + 7 = 4 Reorder the terms: 7 + 9m + 2m2 = 4 Solving 7 + 9m + 2m2 = 4 Solving for variable 'm'. Reorder the terms: 7 + -4 + 9m + 2m2 = 4 + -4 Combine like terms: 7 + -4 = 3 3 + 9m + 2m2 = 4 + -4 Combine like terms: 4 + -4 = 0 3 + 9m + 2m2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + 4.5m + m2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 4.5m + -1.5 + m2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 4.5m + m2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 4.5m + m2 = 0 + -1.5 4.5m + m2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 4.5m + m2 = -1.5 The m term is 4.5m. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5m + 5.0625 + m2 = -1.5 + 5.0625 Reorder the terms: 5.0625 + 4.5m + m2 = -1.5 + 5.0625 Combine like terms: -1.5 + 5.0625 = 3.5625 5.0625 + 4.5m + m2 = 3.5625 Factor a perfect square on the left side: (m + 2.25)(m + 2.25) = 3.5625 Calculate the square root of the right side: 1.887458609 Break this problem into two subproblems by setting (m + 2.25) equal to 1.887458609 and -1.887458609.Subproblem 1
m + 2.25 = 1.887458609 Simplifying m + 2.25 = 1.887458609 Reorder the terms: 2.25 + m = 1.887458609 Solving 2.25 + m = 1.887458609 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + m = 1.887458609 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + m = 1.887458609 + -2.25 m = 1.887458609 + -2.25 Combine like terms: 1.887458609 + -2.25 = -0.362541391 m = -0.362541391 Simplifying m = -0.362541391Subproblem 2
m + 2.25 = -1.887458609 Simplifying m + 2.25 = -1.887458609 Reorder the terms: 2.25 + m = -1.887458609 Solving 2.25 + m = -1.887458609 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + m = -1.887458609 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + m = -1.887458609 + -2.25 m = -1.887458609 + -2.25 Combine like terms: -1.887458609 + -2.25 = -4.137458609 m = -4.137458609 Simplifying m = -4.137458609Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.362541391, -4.137458609}
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