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Simplifying 4m2 + -16m + -49 = 0 Reorder the terms: -49 + -16m + 4m2 = 0 Solving -49 + -16m + 4m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -12.25 + -4m + m2 = 0 Move the constant term to the right: Add '12.25' to each side of the equation. -12.25 + -4m + 12.25 + m2 = 0 + 12.25 Reorder the terms: -12.25 + 12.25 + -4m + m2 = 0 + 12.25 Combine like terms: -12.25 + 12.25 = 0.00 0.00 + -4m + m2 = 0 + 12.25 -4m + m2 = 0 + 12.25 Combine like terms: 0 + 12.25 = 12.25 -4m + m2 = 12.25 The m term is -4m. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4m + 4 + m2 = 12.25 + 4 Reorder the terms: 4 + -4m + m2 = 12.25 + 4 Combine like terms: 12.25 + 4 = 16.25 4 + -4m + m2 = 16.25 Factor a perfect square on the left side: (m + -2)(m + -2) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (m + -2) equal to 4.031128874 and -4.031128874.Subproblem 1
m + -2 = 4.031128874 Simplifying m + -2 = 4.031128874 Reorder the terms: -2 + m = 4.031128874 Solving -2 + m = 4.031128874 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + m = 4.031128874 + 2 Combine like terms: -2 + 2 = 0 0 + m = 4.031128874 + 2 m = 4.031128874 + 2 Combine like terms: 4.031128874 + 2 = 6.031128874 m = 6.031128874 Simplifying m = 6.031128874Subproblem 2
m + -2 = -4.031128874 Simplifying m + -2 = -4.031128874 Reorder the terms: -2 + m = -4.031128874 Solving -2 + m = -4.031128874 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + m = -4.031128874 + 2 Combine like terms: -2 + 2 = 0 0 + m = -4.031128874 + 2 m = -4.031128874 + 2 Combine like terms: -4.031128874 + 2 = -2.031128874 m = -2.031128874 Simplifying m = -2.031128874Solution
The solution to the problem is based on the solutions from the subproblems. m = {6.031128874, -2.031128874}
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