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Simplifying m2 = 14(m + 3) Reorder the terms: m2 = 14(3 + m) m2 = (3 * 14 + m * 14) m2 = (42 + 14m) Solving m2 = 42 + 14m Solving for variable 'm'. Reorder the terms: -42 + -14m + m2 = 42 + 14m + -42 + -14m Reorder the terms: -42 + -14m + m2 = 42 + -42 + 14m + -14m Combine like terms: 42 + -42 = 0 -42 + -14m + m2 = 0 + 14m + -14m -42 + -14m + m2 = 14m + -14m Combine like terms: 14m + -14m = 0 -42 + -14m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + -14m + 42 + m2 = 0 + 42 Reorder the terms: -42 + 42 + -14m + m2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + -14m + m2 = 0 + 42 -14m + m2 = 0 + 42 Combine like terms: 0 + 42 = 42 -14m + m2 = 42 The m term is -14m. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14m + 49 + m2 = 42 + 49 Reorder the terms: 49 + -14m + m2 = 42 + 49 Combine like terms: 42 + 49 = 91 49 + -14m + m2 = 91 Factor a perfect square on the left side: (m + -7)(m + -7) = 91 Calculate the square root of the right side: 9.539392014 Break this problem into two subproblems by setting (m + -7) equal to 9.539392014 and -9.539392014.Subproblem 1
m + -7 = 9.539392014 Simplifying m + -7 = 9.539392014 Reorder the terms: -7 + m = 9.539392014 Solving -7 + m = 9.539392014 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + m = 9.539392014 + 7 Combine like terms: -7 + 7 = 0 0 + m = 9.539392014 + 7 m = 9.539392014 + 7 Combine like terms: 9.539392014 + 7 = 16.539392014 m = 16.539392014 Simplifying m = 16.539392014Subproblem 2
m + -7 = -9.539392014 Simplifying m + -7 = -9.539392014 Reorder the terms: -7 + m = -9.539392014 Solving -7 + m = -9.539392014 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + m = -9.539392014 + 7 Combine like terms: -7 + 7 = 0 0 + m = -9.539392014 + 7 m = -9.539392014 + 7 Combine like terms: -9.539392014 + 7 = -2.539392014 m = -2.539392014 Simplifying m = -2.539392014Solution
The solution to the problem is based on the solutions from the subproblems. m = {16.539392014, -2.539392014}
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