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Simplifying m2 + -17m + -100 = 0 Reorder the terms: -100 + -17m + m2 = 0 Solving -100 + -17m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + -17m + 100 + m2 = 0 + 100 Reorder the terms: -100 + 100 + -17m + m2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -17m + m2 = 0 + 100 -17m + m2 = 0 + 100 Combine like terms: 0 + 100 = 100 -17m + m2 = 100 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 = 100 + 72.25 Reorder the terms: 72.25 + -17m + m2 = 100 + 72.25 Combine like terms: 100 + 72.25 = 172.25 72.25 + -17m + m2 = 172.25 Factor a perfect square on the left side: (m + -8.5)(m + -8.5) = 172.25 Calculate the square root of the right side: 13.124404748 Break this problem into two subproblems by setting (m + -8.5) equal to 13.124404748 and -13.124404748.Subproblem 1
m + -8.5 = 13.124404748 Simplifying m + -8.5 = 13.124404748 Reorder the terms: -8.5 + m = 13.124404748 Solving -8.5 + m = 13.124404748 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 = 13.124404748 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + m = 13.124404748 + 8.5 m = 13.124404748 + 8.5 Combine like terms: 13.124404748 + 8.5 = 21.624404748 m = 21.624404748 Simplifying m = 21.624404748Subproblem 2
m + -8.5 = -13.124404748 Simplifying m + -8.5 = -13.124404748 Reorder the terms: -8.5 + m = -13.124404748 Solving -8.5 + m = -13.124404748 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 = -13.124404748 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + m = -13.124404748 + 8.5 m = -13.124404748 + 8.5 Combine like terms: -13.124404748 + 8.5 = -4.624404748 m = -4.624404748 Simplifying m = -4.624404748Solution
The solution to the problem is based on the solutions from the subproblems. m = {21.624404748, -4.624404748}
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