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Simplifying m2 + -4m = 55 Reorder the terms: -4m + m2 = 55 Solving -4m + m2 = 55 Solving for variable 'm'. Reorder the terms: -55 + -4m + m2 = 55 + -55 Combine like terms: 55 + -55 = 0 -55 + -4m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '55' to each side of the equation. -55 + -4m + 55 + m2 = 0 + 55 Reorder the terms: -55 + 55 + -4m + m2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + -4m + m2 = 0 + 55 -4m + m2 = 0 + 55 Combine like terms: 0 + 55 = 55 -4m + m2 = 55 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 = 55 + 4 Reorder the terms: 4 + -4m + m2 = 55 + 4 Combine like terms: 55 + 4 = 59 4 + -4m + m2 = 59 Factor a perfect square on the left side: (m + -2)(m + -2) = 59 Calculate the square root of the right side: 7.681145748 Break this problem into two subproblems by setting (m + -2) equal to 7.681145748 and -7.681145748.Subproblem 1
m + -2 = 7.681145748 Simplifying m + -2 = 7.681145748 Reorder the terms: -2 + m = 7.681145748 Solving -2 + m = 7.681145748 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 = 7.681145748 + 2 Combine like terms: -2 + 2 = 0 0 + m = 7.681145748 + 2 m = 7.681145748 + 2 Combine like terms: 7.681145748 + 2 = 9.681145748 m = 9.681145748 Simplifying m = 9.681145748Subproblem 2
m + -2 = -7.681145748 Simplifying m + -2 = -7.681145748 Reorder the terms: -2 + m = -7.681145748 Solving -2 + m = -7.681145748 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 = -7.681145748 + 2 Combine like terms: -2 + 2 = 0 0 + m = -7.681145748 + 2 m = -7.681145748 + 2 Combine like terms: -7.681145748 + 2 = -5.681145748 m = -5.681145748 Simplifying m = -5.681145748Solution
The solution to the problem is based on the solutions from the subproblems. m = {9.681145748, -5.681145748}
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