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Simplifying 4m2 = 4m + 19 Reorder the terms: 4m2 = 19 + 4m Solving 4m2 = 19 + 4m Solving for variable 'm'. Reorder the terms: -19 + -4m + 4m2 = 19 + 4m + -19 + -4m Reorder the terms: -19 + -4m + 4m2 = 19 + -19 + 4m + -4m Combine like terms: 19 + -19 = 0 -19 + -4m + 4m2 = 0 + 4m + -4m -19 + -4m + 4m2 = 4m + -4m Combine like terms: 4m + -4m = 0 -19 + -4m + 4m2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.75 + -1m + m2 = 0 Move the constant term to the right: Add '4.75' to each side of the equation. -4.75 + -1m + 4.75 + m2 = 0 + 4.75 Reorder the terms: -4.75 + 4.75 + -1m + m2 = 0 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + -1m + m2 = 0 + 4.75 -1m + m2 = 0 + 4.75 Combine like terms: 0 + 4.75 = 4.75 -1m + m2 = 4.75 The m term is -1m. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1m + 0.25 + m2 = 4.75 + 0.25 Reorder the terms: 0.25 + -1m + m2 = 4.75 + 0.25 Combine like terms: 4.75 + 0.25 = 5 0.25 + -1m + m2 = 5 Factor a perfect square on the left side: (m + -0.5)(m + -0.5) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (m + -0.5) equal to 2.236067978 and -2.236067978.Subproblem 1
m + -0.5 = 2.236067978 Simplifying m + -0.5 = 2.236067978 Reorder the terms: -0.5 + m = 2.236067978 Solving -0.5 + m = 2.236067978 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + m = 2.236067978 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + m = 2.236067978 + 0.5 m = 2.236067978 + 0.5 Combine like terms: 2.236067978 + 0.5 = 2.736067978 m = 2.736067978 Simplifying m = 2.736067978Subproblem 2
m + -0.5 = -2.236067978 Simplifying m + -0.5 = -2.236067978 Reorder the terms: -0.5 + m = -2.236067978 Solving -0.5 + m = -2.236067978 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + m = -2.236067978 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + m = -2.236067978 + 0.5 m = -2.236067978 + 0.5 Combine like terms: -2.236067978 + 0.5 = -1.736067978 m = -1.736067978 Simplifying m = -1.736067978Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.736067978, -1.736067978}
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