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Simplifying 5m2 + -10m + -44 = 7 Reorder the terms: -44 + -10m + 5m2 = 7 Solving -44 + -10m + 5m2 = 7 Solving for variable 'm'. Reorder the terms: -44 + -7 + -10m + 5m2 = 7 + -7 Combine like terms: -44 + -7 = -51 -51 + -10m + 5m2 = 7 + -7 Combine like terms: 7 + -7 = 0 -51 + -10m + 5m2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -10.2 + -2m + m2 = 0 Move the constant term to the right: Add '10.2' to each side of the equation. -10.2 + -2m + 10.2 + m2 = 0 + 10.2 Reorder the terms: -10.2 + 10.2 + -2m + m2 = 0 + 10.2 Combine like terms: -10.2 + 10.2 = 0.0 0.0 + -2m + m2 = 0 + 10.2 -2m + m2 = 0 + 10.2 Combine like terms: 0 + 10.2 = 10.2 -2m + m2 = 10.2 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 = 10.2 + 1 Reorder the terms: 1 + -2m + m2 = 10.2 + 1 Combine like terms: 10.2 + 1 = 11.2 1 + -2m + m2 = 11.2 Factor a perfect square on the left side: (m + -1)(m + -1) = 11.2 Calculate the square root of the right side: 3.346640106 Break this problem into two subproblems by setting (m + -1) equal to 3.346640106 and -3.346640106.Subproblem 1
m + -1 = 3.346640106 Simplifying m + -1 = 3.346640106 Reorder the terms: -1 + m = 3.346640106 Solving -1 + m = 3.346640106 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 = 3.346640106 + 1 Combine like terms: -1 + 1 = 0 0 + m = 3.346640106 + 1 m = 3.346640106 + 1 Combine like terms: 3.346640106 + 1 = 4.346640106 m = 4.346640106 Simplifying m = 4.346640106Subproblem 2
m + -1 = -3.346640106 Simplifying m + -1 = -3.346640106 Reorder the terms: -1 + m = -3.346640106 Solving -1 + m = -3.346640106 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 = -3.346640106 + 1 Combine like terms: -1 + 1 = 0 0 + m = -3.346640106 + 1 m = -3.346640106 + 1 Combine like terms: -3.346640106 + 1 = -2.346640106 m = -2.346640106 Simplifying m = -2.346640106Solution
The solution to the problem is based on the solutions from the subproblems. m = {4.346640106, -2.346640106}
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