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Simplifying m2 + -17m + 47 = 0 Reorder the terms: 47 + -17m + m2 = 0 Solving 47 + -17m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '-47' to each side of the equation. 47 + -17m + -47 + m2 = 0 + -47 Reorder the terms: 47 + -47 + -17m + m2 = 0 + -47 Combine like terms: 47 + -47 = 0 0 + -17m + m2 = 0 + -47 -17m + m2 = 0 + -47 Combine like terms: 0 + -47 = -47 -17m + m2 = -47 The m term is -17m. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17m + 72.25 + m2 = -47 + 72.25 Reorder the terms: 72.25 + -17m + m2 = -47 + 72.25 Combine like terms: -47 + 72.25 = 25.25 72.25 + -17m + m2 = 25.25 Factor a perfect square on the left side: (m + -8.5)(m + -8.5) = 25.25 Calculate the square root of the right side: 5.024937811 Break this problem into two subproblems by setting (m + -8.5) equal to 5.024937811 and -5.024937811.Subproblem 1
m + -8.5 = 5.024937811 Simplifying m + -8.5 = 5.024937811 Reorder the terms: -8.5 + m = 5.024937811 Solving -8.5 + m = 5.024937811 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + m = 5.024937811 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + m = 5.024937811 + 8.5 m = 5.024937811 + 8.5 Combine like terms: 5.024937811 + 8.5 = 13.524937811 m = 13.524937811 Simplifying m = 13.524937811Subproblem 2
m + -8.5 = -5.024937811 Simplifying m + -8.5 = -5.024937811 Reorder the terms: -8.5 + m = -5.024937811 Solving -8.5 + m = -5.024937811 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + m = -5.024937811 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + m = -5.024937811 + 8.5 m = -5.024937811 + 8.5 Combine like terms: -5.024937811 + 8.5 = 3.475062189 m = 3.475062189 Simplifying m = 3.475062189Solution
The solution to the problem is based on the solutions from the subproblems. m = {13.524937811, 3.475062189}
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