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Simplifying m2 + -28m = 11 Reorder the terms: -28m + m2 = 11 Solving -28m + m2 = 11 Solving for variable 'm'. Reorder the terms: -11 + -28m + m2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + -28m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + -28m + 11 + m2 = 0 + 11 Reorder the terms: -11 + 11 + -28m + m2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -28m + m2 = 0 + 11 -28m + m2 = 0 + 11 Combine like terms: 0 + 11 = 11 -28m + m2 = 11 The m term is -28m. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28m + 196 + m2 = 11 + 196 Reorder the terms: 196 + -28m + m2 = 11 + 196 Combine like terms: 11 + 196 = 207 196 + -28m + m2 = 207 Factor a perfect square on the left side: (m + -14)(m + -14) = 207 Calculate the square root of the right side: 14.38749457 Break this problem into two subproblems by setting (m + -14) equal to 14.38749457 and -14.38749457.Subproblem 1
m + -14 = 14.38749457 Simplifying m + -14 = 14.38749457 Reorder the terms: -14 + m = 14.38749457 Solving -14 + m = 14.38749457 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + m = 14.38749457 + 14 Combine like terms: -14 + 14 = 0 0 + m = 14.38749457 + 14 m = 14.38749457 + 14 Combine like terms: 14.38749457 + 14 = 28.38749457 m = 28.38749457 Simplifying m = 28.38749457Subproblem 2
m + -14 = -14.38749457 Simplifying m + -14 = -14.38749457 Reorder the terms: -14 + m = -14.38749457 Solving -14 + m = -14.38749457 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + m = -14.38749457 + 14 Combine like terms: -14 + 14 = 0 0 + m = -14.38749457 + 14 m = -14.38749457 + 14 Combine like terms: -14.38749457 + 14 = -0.38749457 m = -0.38749457 Simplifying m = -0.38749457Solution
The solution to the problem is based on the solutions from the subproblems. m = {28.38749457, -0.38749457}
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