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Simplifying 4m2 + 12m + -11 = 0 Reorder the terms: -11 + 12m + 4m2 = 0 Solving -11 + 12m + 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'. -2.75 + 3m + m2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + 3m + 2.75 + m2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + 3m + m2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + 3m + m2 = 0 + 2.75 3m + m2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 3m + m2 = 2.75 The m term is 3m. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3m + 2.25 + m2 = 2.75 + 2.25 Reorder the terms: 2.25 + 3m + m2 = 2.75 + 2.25 Combine like terms: 2.75 + 2.25 = 5 2.25 + 3m + m2 = 5 Factor a perfect square on the left side: (m + 1.5)(m + 1.5) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (m + 1.5) equal to 2.236067978 and -2.236067978.Subproblem 1
m + 1.5 = 2.236067978 Simplifying m + 1.5 = 2.236067978 Reorder the terms: 1.5 + m = 2.236067978 Solving 1.5 + m = 2.236067978 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + m = 2.236067978 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + m = 2.236067978 + -1.5 m = 2.236067978 + -1.5 Combine like terms: 2.236067978 + -1.5 = 0.736067978 m = 0.736067978 Simplifying m = 0.736067978Subproblem 2
m + 1.5 = -2.236067978 Simplifying m + 1.5 = -2.236067978 Reorder the terms: 1.5 + m = -2.236067978 Solving 1.5 + m = -2.236067978 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + m = -2.236067978 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + m = -2.236067978 + -1.5 m = -2.236067978 + -1.5 Combine like terms: -2.236067978 + -1.5 = -3.736067978 m = -3.736067978 Simplifying m = -3.736067978Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.736067978, -3.736067978}
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