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Simplifying (m2 + -6m + 7) + -1(6m2 + -3) + -1(4m + 4) = 0 Reorder the terms: (7 + -6m + m2) + -1(6m2 + -3) + -1(4m + 4) = 0 Remove parenthesis around (7 + -6m + m2) 7 + -6m + m2 + -1(6m2 + -3) + -1(4m + 4) = 0 Reorder the terms: 7 + -6m + m2 + -1(-3 + 6m2) + -1(4m + 4) = 0 7 + -6m + m2 + (-3 * -1 + 6m2 * -1) + -1(4m + 4) = 0 7 + -6m + m2 + (3 + -6m2) + -1(4m + 4) = 0 Reorder the terms: 7 + -6m + m2 + 3 + -6m2 + -1(4 + 4m) = 0 7 + -6m + m2 + 3 + -6m2 + (4 * -1 + 4m * -1) = 0 7 + -6m + m2 + 3 + -6m2 + (-4 + -4m) = 0 Reorder the terms: 7 + 3 + -4 + -6m + -4m + m2 + -6m2 = 0 Combine like terms: 7 + 3 = 10 10 + -4 + -6m + -4m + m2 + -6m2 = 0 Combine like terms: 10 + -4 = 6 6 + -6m + -4m + m2 + -6m2 = 0 Combine like terms: -6m + -4m = -10m 6 + -10m + m2 + -6m2 = 0 Combine like terms: m2 + -6m2 = -5m2 6 + -10m + -5m2 = 0 Solving 6 + -10m + -5m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1.2 + 2m + m2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + 2m + 1.2 + m2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + 2m + m2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + 2m + m2 = 0 + 1.2 2m + m2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 2m + m2 = 1.2 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 = 1.2 + 1 Reorder the terms: 1 + 2m + m2 = 1.2 + 1 Combine like terms: 1.2 + 1 = 2.2 1 + 2m + m2 = 2.2 Factor a perfect square on the left side: (m + 1)(m + 1) = 2.2 Calculate the square root of the right side: 1.483239697 Break this problem into two subproblems by setting (m + 1) equal to 1.483239697 and -1.483239697.Subproblem 1
m + 1 = 1.483239697 Simplifying m + 1 = 1.483239697 Reorder the terms: 1 + m = 1.483239697 Solving 1 + m = 1.483239697 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 = 1.483239697 + -1 Combine like terms: 1 + -1 = 0 0 + m = 1.483239697 + -1 m = 1.483239697 + -1 Combine like terms: 1.483239697 + -1 = 0.483239697 m = 0.483239697 Simplifying m = 0.483239697Subproblem 2
m + 1 = -1.483239697 Simplifying m + 1 = -1.483239697 Reorder the terms: 1 + m = -1.483239697 Solving 1 + m = -1.483239697 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 = -1.483239697 + -1 Combine like terms: 1 + -1 = 0 0 + m = -1.483239697 + -1 m = -1.483239697 + -1 Combine like terms: -1.483239697 + -1 = -2.483239697 m = -2.483239697 Simplifying m = -2.483239697Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.483239697, -2.483239697}
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