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Simplifying 4m2 + -27m + -4 = 0 Reorder the terms: -4 + -27m + 4m2 = 0 Solving -4 + -27m + 4m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1 + -6.75m + m2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -6.75m + 1 + m2 = 0 + 1 Reorder the terms: -1 + 1 + -6.75m + m2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -6.75m + m2 = 0 + 1 -6.75m + m2 = 0 + 1 Combine like terms: 0 + 1 = 1 -6.75m + m2 = 1 The m term is -6.75m. Take half its coefficient (-3.375). Square it (11.390625) and add it to both sides. Add '11.390625' to each side of the equation. -6.75m + 11.390625 + m2 = 1 + 11.390625 Reorder the terms: 11.390625 + -6.75m + m2 = 1 + 11.390625 Combine like terms: 1 + 11.390625 = 12.390625 11.390625 + -6.75m + m2 = 12.390625 Factor a perfect square on the left side: (m + -3.375)(m + -3.375) = 12.390625 Calculate the square root of the right side: 3.52003196 Break this problem into two subproblems by setting (m + -3.375) equal to 3.52003196 and -3.52003196.Subproblem 1
m + -3.375 = 3.52003196 Simplifying m + -3.375 = 3.52003196 Reorder the terms: -3.375 + m = 3.52003196 Solving -3.375 + m = 3.52003196 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + m = 3.52003196 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + m = 3.52003196 + 3.375 m = 3.52003196 + 3.375 Combine like terms: 3.52003196 + 3.375 = 6.89503196 m = 6.89503196 Simplifying m = 6.89503196Subproblem 2
m + -3.375 = -3.52003196 Simplifying m + -3.375 = -3.52003196 Reorder the terms: -3.375 + m = -3.52003196 Solving -3.375 + m = -3.52003196 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + m = -3.52003196 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + m = -3.52003196 + 3.375 m = -3.52003196 + 3.375 Combine like terms: -3.52003196 + 3.375 = -0.14503196 m = -0.14503196 Simplifying m = -0.14503196Solution
The solution to the problem is based on the solutions from the subproblems. m = {6.89503196, -0.14503196}
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