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Simplifying 7m2 + 4m + -2 = 0 Reorder the terms: -2 + 4m + 7m2 = 0 Solving -2 + 4m + 7m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.2857142857 + 0.5714285714m + m2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.5714285714m + 0.2857142857 + m2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + 0.5714285714m + m2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + 0.5714285714m + m2 = 0 + 0.2857142857 0.5714285714m + m2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 0.5714285714m + m2 = 0.2857142857 The m term is 0.5714285714m. Take half its coefficient (0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. 0.5714285714m + 0.08163265305 + m2 = 0.2857142857 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714m + m2 = 0.2857142857 + 0.08163265305 Combine like terms: 0.2857142857 + 0.08163265305 = 0.36734693875 0.08163265305 + 0.5714285714m + m2 = 0.36734693875 Factor a perfect square on the left side: (m + 0.2857142857)(m + 0.2857142857) = 0.36734693875 Calculate the square root of the right side: 0.606091527 Break this problem into two subproblems by setting (m + 0.2857142857) equal to 0.606091527 and -0.606091527.Subproblem 1
m + 0.2857142857 = 0.606091527 Simplifying m + 0.2857142857 = 0.606091527 Reorder the terms: 0.2857142857 + m = 0.606091527 Solving 0.2857142857 + m = 0.606091527 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + m = 0.606091527 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + m = 0.606091527 + -0.2857142857 m = 0.606091527 + -0.2857142857 Combine like terms: 0.606091527 + -0.2857142857 = 0.3203772413 m = 0.3203772413 Simplifying m = 0.3203772413Subproblem 2
m + 0.2857142857 = -0.606091527 Simplifying m + 0.2857142857 = -0.606091527 Reorder the terms: 0.2857142857 + m = -0.606091527 Solving 0.2857142857 + m = -0.606091527 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + m = -0.606091527 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + m = -0.606091527 + -0.2857142857 m = -0.606091527 + -0.2857142857 Combine like terms: -0.606091527 + -0.2857142857 = -0.8918058127 m = -0.8918058127 Simplifying m = -0.8918058127Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.3203772413, -0.8918058127}
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