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Simplifying 7m2 + -14m + -27 = 0 Reorder the terms: -27 + -14m + 7m2 = 0 Solving -27 + -14m + 7m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -3.857142857 + -2m + m2 = 0 Move the constant term to the right: Add '3.857142857' to each side of the equation. -3.857142857 + -2m + 3.857142857 + m2 = 0 + 3.857142857 Reorder the terms: -3.857142857 + 3.857142857 + -2m + m2 = 0 + 3.857142857 Combine like terms: -3.857142857 + 3.857142857 = 0.000000000 0.000000000 + -2m + m2 = 0 + 3.857142857 -2m + m2 = 0 + 3.857142857 Combine like terms: 0 + 3.857142857 = 3.857142857 -2m + m2 = 3.857142857 The m term is -2m. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2m + 1 + m2 = 3.857142857 + 1 Reorder the terms: 1 + -2m + m2 = 3.857142857 + 1 Combine like terms: 3.857142857 + 1 = 4.857142857 1 + -2m + m2 = 4.857142857 Factor a perfect square on the left side: (m + -1)(m + -1) = 4.857142857 Calculate the square root of the right side: 2.20389266 Break this problem into two subproblems by setting (m + -1) equal to 2.20389266 and -2.20389266.Subproblem 1
m + -1 = 2.20389266 Simplifying m + -1 = 2.20389266 Reorder the terms: -1 + m = 2.20389266 Solving -1 + m = 2.20389266 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + m = 2.20389266 + 1 Combine like terms: -1 + 1 = 0 0 + m = 2.20389266 + 1 m = 2.20389266 + 1 Combine like terms: 2.20389266 + 1 = 3.20389266 m = 3.20389266 Simplifying m = 3.20389266Subproblem 2
m + -1 = -2.20389266 Simplifying m + -1 = -2.20389266 Reorder the terms: -1 + m = -2.20389266 Solving -1 + m = -2.20389266 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + m = -2.20389266 + 1 Combine like terms: -1 + 1 = 0 0 + m = -2.20389266 + 1 m = -2.20389266 + 1 Combine like terms: -2.20389266 + 1 = -1.20389266 m = -1.20389266 Simplifying m = -1.20389266Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.20389266, -1.20389266}
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