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Simplifying m2 + 4m + -11 = (2m + 10)(m + -2) Reorder the terms: -11 + 4m + m2 = (2m + 10)(m + -2) Reorder the terms: -11 + 4m + m2 = (10 + 2m)(m + -2) Reorder the terms: -11 + 4m + m2 = (10 + 2m)(-2 + m) Multiply (10 + 2m) * (-2 + m) -11 + 4m + m2 = (10(-2 + m) + 2m * (-2 + m)) -11 + 4m + m2 = ((-2 * 10 + m * 10) + 2m * (-2 + m)) -11 + 4m + m2 = ((-20 + 10m) + 2m * (-2 + m)) -11 + 4m + m2 = (-20 + 10m + (-2 * 2m + m * 2m)) -11 + 4m + m2 = (-20 + 10m + (-4m + 2m2)) Combine like terms: 10m + -4m = 6m -11 + 4m + m2 = (-20 + 6m + 2m2) Solving -11 + 4m + m2 = -20 + 6m + 2m2 Solving for variable 'm'. Reorder the terms: -11 + 20 + 4m + -6m + m2 + -2m2 = -20 + 6m + 2m2 + 20 + -6m + -2m2 Combine like terms: -11 + 20 = 9 9 + 4m + -6m + m2 + -2m2 = -20 + 6m + 2m2 + 20 + -6m + -2m2 Combine like terms: 4m + -6m = -2m 9 + -2m + m2 + -2m2 = -20 + 6m + 2m2 + 20 + -6m + -2m2 Combine like terms: m2 + -2m2 = -1m2 9 + -2m + -1m2 = -20 + 6m + 2m2 + 20 + -6m + -2m2 Reorder the terms: 9 + -2m + -1m2 = -20 + 20 + 6m + -6m + 2m2 + -2m2 Combine like terms: -20 + 20 = 0 9 + -2m + -1m2 = 0 + 6m + -6m + 2m2 + -2m2 9 + -2m + -1m2 = 6m + -6m + 2m2 + -2m2 Combine like terms: 6m + -6m = 0 9 + -2m + -1m2 = 0 + 2m2 + -2m2 9 + -2m + -1m2 = 2m2 + -2m2 Combine like terms: 2m2 + -2m2 = 0 9 + -2m + -1m2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -9 + 2m + m2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 2m + 9 + m2 = 0 + 9 Reorder the terms: -9 + 9 + 2m + m2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 2m + m2 = 0 + 9 2m + m2 = 0 + 9 Combine like terms: 0 + 9 = 9 2m + m2 = 9 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 = 9 + 1 Reorder the terms: 1 + 2m + m2 = 9 + 1 Combine like terms: 9 + 1 = 10 1 + 2m + m2 = 10 Factor a perfect square on the left side: (m + 1)(m + 1) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (m + 1) equal to 3.16227766 and -3.16227766.Subproblem 1
m + 1 = 3.16227766 Simplifying m + 1 = 3.16227766 Reorder the terms: 1 + m = 3.16227766 Solving 1 + m = 3.16227766 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 = 3.16227766 + -1 Combine like terms: 1 + -1 = 0 0 + m = 3.16227766 + -1 m = 3.16227766 + -1 Combine like terms: 3.16227766 + -1 = 2.16227766 m = 2.16227766 Simplifying m = 2.16227766Subproblem 2
m + 1 = -3.16227766 Simplifying m + 1 = -3.16227766 Reorder the terms: 1 + m = -3.16227766 Solving 1 + m = -3.16227766 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 = -3.16227766 + -1 Combine like terms: 1 + -1 = 0 0 + m = -3.16227766 + -1 m = -3.16227766 + -1 Combine like terms: -3.16227766 + -1 = -4.16227766 m = -4.16227766 Simplifying m = -4.16227766Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.16227766, -4.16227766}
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