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Simplifying 0 = m2 + -110m + -2500 Reorder the terms: 0 = -2500 + -110m + m2 Solving 0 = -2500 + -110m + m2 Solving for variable 'm'. Combine like terms: 0 + 2500 = 2500 2500 + 110m + -1m2 = -2500 + -110m + m2 + 2500 + 110m + -1m2 Reorder the terms: 2500 + 110m + -1m2 = -2500 + 2500 + -110m + 110m + m2 + -1m2 Combine like terms: -2500 + 2500 = 0 2500 + 110m + -1m2 = 0 + -110m + 110m + m2 + -1m2 2500 + 110m + -1m2 = -110m + 110m + m2 + -1m2 Combine like terms: -110m + 110m = 0 2500 + 110m + -1m2 = 0 + m2 + -1m2 2500 + 110m + -1m2 = m2 + -1m2 Combine like terms: m2 + -1m2 = 0 2500 + 110m + -1m2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2500 + -110m + m2 = 0 Move the constant term to the right: Add '2500' to each side of the equation. -2500 + -110m + 2500 + m2 = 0 + 2500 Reorder the terms: -2500 + 2500 + -110m + m2 = 0 + 2500 Combine like terms: -2500 + 2500 = 0 0 + -110m + m2 = 0 + 2500 -110m + m2 = 0 + 2500 Combine like terms: 0 + 2500 = 2500 -110m + m2 = 2500 The m term is -110m. Take half its coefficient (-55). Square it (3025) and add it to both sides. Add '3025' to each side of the equation. -110m + 3025 + m2 = 2500 + 3025 Reorder the terms: 3025 + -110m + m2 = 2500 + 3025 Combine like terms: 2500 + 3025 = 5525 3025 + -110m + m2 = 5525 Factor a perfect square on the left side: (m + -55)(m + -55) = 5525 Calculate the square root of the right side: 74.330343737 Break this problem into two subproblems by setting (m + -55) equal to 74.330343737 and -74.330343737.Subproblem 1
m + -55 = 74.330343737 Simplifying m + -55 = 74.330343737 Reorder the terms: -55 + m = 74.330343737 Solving -55 + m = 74.330343737 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '55' to each side of the equation. -55 + 55 + m = 74.330343737 + 55 Combine like terms: -55 + 55 = 0 0 + m = 74.330343737 + 55 m = 74.330343737 + 55 Combine like terms: 74.330343737 + 55 = 129.330343737 m = 129.330343737 Simplifying m = 129.330343737Subproblem 2
m + -55 = -74.330343737 Simplifying m + -55 = -74.330343737 Reorder the terms: -55 + m = -74.330343737 Solving -55 + m = -74.330343737 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '55' to each side of the equation. -55 + 55 + m = -74.330343737 + 55 Combine like terms: -55 + 55 = 0 0 + m = -74.330343737 + 55 m = -74.330343737 + 55 Combine like terms: -74.330343737 + 55 = -19.330343737 m = -19.330343737 Simplifying m = -19.330343737Solution
The solution to the problem is based on the solutions from the subproblems. m = {129.330343737, -19.330343737}
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