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Simplifying 5m2 + 10m + -80 = 7 Reorder the terms: -80 + 10m + 5m2 = 7 Solving -80 + 10m + 5m2 = 7 Solving for variable 'm'. Reorder the terms: -80 + -7 + 10m + 5m2 = 7 + -7 Combine like terms: -80 + -7 = -87 -87 + 10m + 5m2 = 7 + -7 Combine like terms: 7 + -7 = 0 -87 + 10m + 5m2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -17.4 + 2m + m2 = 0 Move the constant term to the right: Add '17.4' to each side of the equation. -17.4 + 2m + 17.4 + m2 = 0 + 17.4 Reorder the terms: -17.4 + 17.4 + 2m + m2 = 0 + 17.4 Combine like terms: -17.4 + 17.4 = 0.0 0.0 + 2m + m2 = 0 + 17.4 2m + m2 = 0 + 17.4 Combine like terms: 0 + 17.4 = 17.4 2m + m2 = 17.4 The m term is 2m. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2m + 1 + m2 = 17.4 + 1 Reorder the terms: 1 + 2m + m2 = 17.4 + 1 Combine like terms: 17.4 + 1 = 18.4 1 + 2m + m2 = 18.4 Factor a perfect square on the left side: (m + 1)(m + 1) = 18.4 Calculate the square root of the right side: 4.289522118 Break this problem into two subproblems by setting (m + 1) equal to 4.289522118 and -4.289522118.Subproblem 1
m + 1 = 4.289522118 Simplifying m + 1 = 4.289522118 Reorder the terms: 1 + m = 4.289522118 Solving 1 + m = 4.289522118 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + m = 4.289522118 + -1 Combine like terms: 1 + -1 = 0 0 + m = 4.289522118 + -1 m = 4.289522118 + -1 Combine like terms: 4.289522118 + -1 = 3.289522118 m = 3.289522118 Simplifying m = 3.289522118Subproblem 2
m + 1 = -4.289522118 Simplifying m + 1 = -4.289522118 Reorder the terms: 1 + m = -4.289522118 Solving 1 + m = -4.289522118 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + m = -4.289522118 + -1 Combine like terms: 1 + -1 = 0 0 + m = -4.289522118 + -1 m = -4.289522118 + -1 Combine like terms: -4.289522118 + -1 = -5.289522118 m = -5.289522118 Simplifying m = -5.289522118Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.289522118, -5.289522118}
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