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Simplifying 28m2 + -3m + -28 = 0 Reorder the terms: -28 + -3m + 28m2 = 0 Solving -28 + -3m + 28m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -1 + -0.1071428571m + m2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.1071428571m + 1 + m2 = 0 + 1 Reorder the terms: -1 + 1 + -0.1071428571m + m2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.1071428571m + m2 = 0 + 1 -0.1071428571m + m2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.1071428571m + m2 = 1 The m term is -0.1071428571m. Take half its coefficient (-0.05357142855). Square it (0.002869897957) and add it to both sides. Add '0.002869897957' to each side of the equation. -0.1071428571m + 0.002869897957 + m2 = 1 + 0.002869897957 Reorder the terms: 0.002869897957 + -0.1071428571m + m2 = 1 + 0.002869897957 Combine like terms: 1 + 0.002869897957 = 1.002869897957 0.002869897957 + -0.1071428571m + m2 = 1.002869897957 Factor a perfect square on the left side: (m + -0.05357142855)(m + -0.05357142855) = 1.002869897957 Calculate the square root of the right side: 1.001433921 Break this problem into two subproblems by setting (m + -0.05357142855) equal to 1.001433921 and -1.001433921.Subproblem 1
m + -0.05357142855 = 1.001433921 Simplifying m + -0.05357142855 = 1.001433921 Reorder the terms: -0.05357142855 + m = 1.001433921 Solving -0.05357142855 + m = 1.001433921 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.05357142855' to each side of the equation. -0.05357142855 + 0.05357142855 + m = 1.001433921 + 0.05357142855 Combine like terms: -0.05357142855 + 0.05357142855 = 0.00000000000 0.00000000000 + m = 1.001433921 + 0.05357142855 m = 1.001433921 + 0.05357142855 Combine like terms: 1.001433921 + 0.05357142855 = 1.05500534955 m = 1.05500534955 Simplifying m = 1.05500534955Subproblem 2
m + -0.05357142855 = -1.001433921 Simplifying m + -0.05357142855 = -1.001433921 Reorder the terms: -0.05357142855 + m = -1.001433921 Solving -0.05357142855 + m = -1.001433921 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.05357142855' to each side of the equation. -0.05357142855 + 0.05357142855 + m = -1.001433921 + 0.05357142855 Combine like terms: -0.05357142855 + 0.05357142855 = 0.00000000000 0.00000000000 + m = -1.001433921 + 0.05357142855 m = -1.001433921 + 0.05357142855 Combine like terms: -1.001433921 + 0.05357142855 = -0.94786249245 m = -0.94786249245 Simplifying m = -0.94786249245Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.05500534955, -0.94786249245}
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