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Simplifying 11m2 + -11 = 3m Reorder the terms: -11 + 11m2 = 3m Solving -11 + 11m2 = 3m Solving for variable 'm'. Reorder the terms: -11 + -3m + 11m2 = 3m + -3m Combine like terms: 3m + -3m = 0 -11 + -3m + 11m2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -1 + -0.2727272727m + m2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.2727272727m + 1 + m2 = 0 + 1 Reorder the terms: -1 + 1 + -0.2727272727m + m2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.2727272727m + m2 = 0 + 1 -0.2727272727m + m2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.2727272727m + m2 = 1 The m term is -0.2727272727m. Take half its coefficient (-0.1363636364). Square it (0.01859504133) and add it to both sides. Add '0.01859504133' to each side of the equation. -0.2727272727m + 0.01859504133 + m2 = 1 + 0.01859504133 Reorder the terms: 0.01859504133 + -0.2727272727m + m2 = 1 + 0.01859504133 Combine like terms: 1 + 0.01859504133 = 1.01859504133 0.01859504133 + -0.2727272727m + m2 = 1.01859504133 Factor a perfect square on the left side: (m + -0.1363636364)(m + -0.1363636364) = 1.01859504133 Calculate the square root of the right side: 1.009254696 Break this problem into two subproblems by setting (m + -0.1363636364) equal to 1.009254696 and -1.009254696.Subproblem 1
m + -0.1363636364 = 1.009254696 Simplifying m + -0.1363636364 = 1.009254696 Reorder the terms: -0.1363636364 + m = 1.009254696 Solving -0.1363636364 + m = 1.009254696 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.1363636364' to each side of the equation. -0.1363636364 + 0.1363636364 + m = 1.009254696 + 0.1363636364 Combine like terms: -0.1363636364 + 0.1363636364 = 0.0000000000 0.0000000000 + m = 1.009254696 + 0.1363636364 m = 1.009254696 + 0.1363636364 Combine like terms: 1.009254696 + 0.1363636364 = 1.1456183324 m = 1.1456183324 Simplifying m = 1.1456183324Subproblem 2
m + -0.1363636364 = -1.009254696 Simplifying m + -0.1363636364 = -1.009254696 Reorder the terms: -0.1363636364 + m = -1.009254696 Solving -0.1363636364 + m = -1.009254696 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.1363636364' to each side of the equation. -0.1363636364 + 0.1363636364 + m = -1.009254696 + 0.1363636364 Combine like terms: -0.1363636364 + 0.1363636364 = 0.0000000000 0.0000000000 + m = -1.009254696 + 0.1363636364 m = -1.009254696 + 0.1363636364 Combine like terms: -1.009254696 + 0.1363636364 = -0.8728910596 m = -0.8728910596 Simplifying m = -0.8728910596Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.1456183324, -0.8728910596}
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