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Simplifying 25m2 + -10m + -111 = 0 Reorder the terms: -111 + -10m + 25m2 = 0 Solving -111 + -10m + 25m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -4.44 + -0.4m + m2 = 0 Move the constant term to the right: Add '4.44' to each side of the equation. -4.44 + -0.4m + 4.44 + m2 = 0 + 4.44 Reorder the terms: -4.44 + 4.44 + -0.4m + m2 = 0 + 4.44 Combine like terms: -4.44 + 4.44 = 0.00 0.00 + -0.4m + m2 = 0 + 4.44 -0.4m + m2 = 0 + 4.44 Combine like terms: 0 + 4.44 = 4.44 -0.4m + m2 = 4.44 The m term is -0.4m. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4m + 0.04 + m2 = 4.44 + 0.04 Reorder the terms: 0.04 + -0.4m + m2 = 4.44 + 0.04 Combine like terms: 4.44 + 0.04 = 4.48 0.04 + -0.4m + m2 = 4.48 Factor a perfect square on the left side: (m + -0.2)(m + -0.2) = 4.48 Calculate the square root of the right side: 2.116601049 Break this problem into two subproblems by setting (m + -0.2) equal to 2.116601049 and -2.116601049.Subproblem 1
m + -0.2 = 2.116601049 Simplifying m + -0.2 = 2.116601049 Reorder the terms: -0.2 + m = 2.116601049 Solving -0.2 + m = 2.116601049 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + m = 2.116601049 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + m = 2.116601049 + 0.2 m = 2.116601049 + 0.2 Combine like terms: 2.116601049 + 0.2 = 2.316601049 m = 2.316601049 Simplifying m = 2.316601049Subproblem 2
m + -0.2 = -2.116601049 Simplifying m + -0.2 = -2.116601049 Reorder the terms: -0.2 + m = -2.116601049 Solving -0.2 + m = -2.116601049 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + m = -2.116601049 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + m = -2.116601049 + 0.2 m = -2.116601049 + 0.2 Combine like terms: -2.116601049 + 0.2 = -1.916601049 m = -1.916601049 Simplifying m = -1.916601049Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.316601049, -1.916601049}
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