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Simplifying m2 + -4m + -93 = 0 Reorder the terms: -93 + -4m + m2 = 0 Solving -93 + -4m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '93' to each side of the equation. -93 + -4m + 93 + m2 = 0 + 93 Reorder the terms: -93 + 93 + -4m + m2 = 0 + 93 Combine like terms: -93 + 93 = 0 0 + -4m + m2 = 0 + 93 -4m + m2 = 0 + 93 Combine like terms: 0 + 93 = 93 -4m + m2 = 93 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 = 93 + 4 Reorder the terms: 4 + -4m + m2 = 93 + 4 Combine like terms: 93 + 4 = 97 4 + -4m + m2 = 97 Factor a perfect square on the left side: (m + -2)(m + -2) = 97 Calculate the square root of the right side: 9.848857802 Break this problem into two subproblems by setting (m + -2) equal to 9.848857802 and -9.848857802.Subproblem 1
m + -2 = 9.848857802 Simplifying m + -2 = 9.848857802 Reorder the terms: -2 + m = 9.848857802 Solving -2 + m = 9.848857802 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 = 9.848857802 + 2 Combine like terms: -2 + 2 = 0 0 + m = 9.848857802 + 2 m = 9.848857802 + 2 Combine like terms: 9.848857802 + 2 = 11.848857802 m = 11.848857802 Simplifying m = 11.848857802Subproblem 2
m + -2 = -9.848857802 Simplifying m + -2 = -9.848857802 Reorder the terms: -2 + m = -9.848857802 Solving -2 + m = -9.848857802 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 = -9.848857802 + 2 Combine like terms: -2 + 2 = 0 0 + m = -9.848857802 + 2 m = -9.848857802 + 2 Combine like terms: -9.848857802 + 2 = -7.848857802 m = -7.848857802 Simplifying m = -7.848857802Solution
The solution to the problem is based on the solutions from the subproblems. m = {11.848857802, -7.848857802}
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