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Simplifying 7 = m2 + -4m Reorder the terms: 7 = -4m + m2 Solving 7 = -4m + m2 Solving for variable 'm'. Reorder the terms: 7 + 4m + -1m2 = -4m + 4m + m2 + -1m2 Combine like terms: -4m + 4m = 0 7 + 4m + -1m2 = 0 + m2 + -1m2 7 + 4m + -1m2 = m2 + -1m2 Combine like terms: m2 + -1m2 = 0 7 + 4m + -1m2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -7 + -4m + m2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -4m + 7 + m2 = 0 + 7 Reorder the terms: -7 + 7 + -4m + m2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -4m + m2 = 0 + 7 -4m + m2 = 0 + 7 Combine like terms: 0 + 7 = 7 -4m + m2 = 7 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 = 7 + 4 Reorder the terms: 4 + -4m + m2 = 7 + 4 Combine like terms: 7 + 4 = 11 4 + -4m + m2 = 11 Factor a perfect square on the left side: (m + -2)(m + -2) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (m + -2) equal to 3.31662479 and -3.31662479.Subproblem 1
m + -2 = 3.31662479 Simplifying m + -2 = 3.31662479 Reorder the terms: -2 + m = 3.31662479 Solving -2 + m = 3.31662479 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 = 3.31662479 + 2 Combine like terms: -2 + 2 = 0 0 + m = 3.31662479 + 2 m = 3.31662479 + 2 Combine like terms: 3.31662479 + 2 = 5.31662479 m = 5.31662479 Simplifying m = 5.31662479Subproblem 2
m + -2 = -3.31662479 Simplifying m + -2 = -3.31662479 Reorder the terms: -2 + m = -3.31662479 Solving -2 + m = -3.31662479 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 = -3.31662479 + 2 Combine like terms: -2 + 2 = 0 0 + m = -3.31662479 + 2 m = -3.31662479 + 2 Combine like terms: -3.31662479 + 2 = -1.31662479 m = -1.31662479 Simplifying m = -1.31662479Solution
The solution to the problem is based on the solutions from the subproblems. m = {5.31662479, -1.31662479}
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