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Simplifying 4m2 + -4m + -43 = 0 Reorder the terms: -43 + -4m + 4m2 = 0 Solving -43 + -4m + 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'. -10.75 + -1m + m2 = 0 Move the constant term to the right: Add '10.75' to each side of the equation. -10.75 + -1m + 10.75 + m2 = 0 + 10.75 Reorder the terms: -10.75 + 10.75 + -1m + m2 = 0 + 10.75 Combine like terms: -10.75 + 10.75 = 0.00 0.00 + -1m + m2 = 0 + 10.75 -1m + m2 = 0 + 10.75 Combine like terms: 0 + 10.75 = 10.75 -1m + m2 = 10.75 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 = 10.75 + 0.25 Reorder the terms: 0.25 + -1m + m2 = 10.75 + 0.25 Combine like terms: 10.75 + 0.25 = 11 0.25 + -1m + m2 = 11 Factor a perfect square on the left side: (m + -0.5)(m + -0.5) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (m + -0.5) equal to 3.31662479 and -3.31662479.Subproblem 1
m + -0.5 = 3.31662479 Simplifying m + -0.5 = 3.31662479 Reorder the terms: -0.5 + m = 3.31662479 Solving -0.5 + m = 3.31662479 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 = 3.31662479 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + m = 3.31662479 + 0.5 m = 3.31662479 + 0.5 Combine like terms: 3.31662479 + 0.5 = 3.81662479 m = 3.81662479 Simplifying m = 3.81662479Subproblem 2
m + -0.5 = -3.31662479 Simplifying m + -0.5 = -3.31662479 Reorder the terms: -0.5 + m = -3.31662479 Solving -0.5 + m = -3.31662479 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 = -3.31662479 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + m = -3.31662479 + 0.5 m = -3.31662479 + 0.5 Combine like terms: -3.31662479 + 0.5 = -2.81662479 m = -2.81662479 Simplifying m = -2.81662479Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.81662479, -2.81662479}
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