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Simplifying m2 + 4m + -89 = 0 Reorder the terms: -89 + 4m + m2 = 0 Solving -89 + 4m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '89' to each side of the equation. -89 + 4m + 89 + m2 = 0 + 89 Reorder the terms: -89 + 89 + 4m + m2 = 0 + 89 Combine like terms: -89 + 89 = 0 0 + 4m + m2 = 0 + 89 4m + m2 = 0 + 89 Combine like terms: 0 + 89 = 89 4m + m2 = 89 The m term is 4m. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4m + 4 + m2 = 89 + 4 Reorder the terms: 4 + 4m + m2 = 89 + 4 Combine like terms: 89 + 4 = 93 4 + 4m + m2 = 93 Factor a perfect square on the left side: (m + 2)(m + 2) = 93 Calculate the square root of the right side: 9.643650761 Break this problem into two subproblems by setting (m + 2) equal to 9.643650761 and -9.643650761.Subproblem 1
m + 2 = 9.643650761 Simplifying m + 2 = 9.643650761 Reorder the terms: 2 + m = 9.643650761 Solving 2 + m = 9.643650761 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + m = 9.643650761 + -2 Combine like terms: 2 + -2 = 0 0 + m = 9.643650761 + -2 m = 9.643650761 + -2 Combine like terms: 9.643650761 + -2 = 7.643650761 m = 7.643650761 Simplifying m = 7.643650761Subproblem 2
m + 2 = -9.643650761 Simplifying m + 2 = -9.643650761 Reorder the terms: 2 + m = -9.643650761 Solving 2 + m = -9.643650761 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + m = -9.643650761 + -2 Combine like terms: 2 + -2 = 0 0 + m = -9.643650761 + -2 m = -9.643650761 + -2 Combine like terms: -9.643650761 + -2 = -11.643650761 m = -11.643650761 Simplifying m = -11.643650761Solution
The solution to the problem is based on the solutions from the subproblems. m = {7.643650761, -11.643650761}
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