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Simplifying 11m(6m + -5) = 25 Reorder the terms: 11m(-5 + 6m) = 25 (-5 * 11m + 6m * 11m) = 25 (-55m + 66m2) = 25 Solving -55m + 66m2 = 25 Solving for variable 'm'. Reorder the terms: -25 + -55m + 66m2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + -55m + 66m2 = 0 Begin completing the square. Divide all terms by 66 the coefficient of the squared term: Divide each side by '66'. -0.3787878788 + -0.8333333333m + m2 = 0 Move the constant term to the right: Add '0.3787878788' to each side of the equation. -0.3787878788 + -0.8333333333m + 0.3787878788 + m2 = 0 + 0.3787878788 Reorder the terms: -0.3787878788 + 0.3787878788 + -0.8333333333m + m2 = 0 + 0.3787878788 Combine like terms: -0.3787878788 + 0.3787878788 = 0.0000000000 0.0000000000 + -0.8333333333m + m2 = 0 + 0.3787878788 -0.8333333333m + m2 = 0 + 0.3787878788 Combine like terms: 0 + 0.3787878788 = 0.3787878788 -0.8333333333m + m2 = 0.3787878788 The m term is -0.8333333333m. Take half its coefficient (-0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. -0.8333333333m + 0.1736111111 + m2 = 0.3787878788 + 0.1736111111 Reorder the terms: 0.1736111111 + -0.8333333333m + m2 = 0.3787878788 + 0.1736111111 Combine like terms: 0.3787878788 + 0.1736111111 = 0.5523989899 0.1736111111 + -0.8333333333m + m2 = 0.5523989899 Factor a perfect square on the left side: (m + -0.4166666667)(m + -0.4166666667) = 0.5523989899 Calculate the square root of the right side: 0.743235488 Break this problem into two subproblems by setting (m + -0.4166666667) equal to 0.743235488 and -0.743235488.Subproblem 1
m + -0.4166666667 = 0.743235488 Simplifying m + -0.4166666667 = 0.743235488 Reorder the terms: -0.4166666667 + m = 0.743235488 Solving -0.4166666667 + m = 0.743235488 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + m = 0.743235488 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + m = 0.743235488 + 0.4166666667 m = 0.743235488 + 0.4166666667 Combine like terms: 0.743235488 + 0.4166666667 = 1.1599021547 m = 1.1599021547 Simplifying m = 1.1599021547Subproblem 2
m + -0.4166666667 = -0.743235488 Simplifying m + -0.4166666667 = -0.743235488 Reorder the terms: -0.4166666667 + m = -0.743235488 Solving -0.4166666667 + m = -0.743235488 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + m = -0.743235488 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + m = -0.743235488 + 0.4166666667 m = -0.743235488 + 0.4166666667 Combine like terms: -0.743235488 + 0.4166666667 = -0.3265688213 m = -0.3265688213 Simplifying m = -0.3265688213Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.1599021547, -0.3265688213}
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