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Simplifying 14m2 + 17m + -33 = 0 Reorder the terms: -33 + 17m + 14m2 = 0 Solving -33 + 17m + 14m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -2.357142857 + 1.214285714m + m2 = 0 Move the constant term to the right: Add '2.357142857' to each side of the equation. -2.357142857 + 1.214285714m + 2.357142857 + m2 = 0 + 2.357142857 Reorder the terms: -2.357142857 + 2.357142857 + 1.214285714m + m2 = 0 + 2.357142857 Combine like terms: -2.357142857 + 2.357142857 = 0.000000000 0.000000000 + 1.214285714m + m2 = 0 + 2.357142857 1.214285714m + m2 = 0 + 2.357142857 Combine like terms: 0 + 2.357142857 = 2.357142857 1.214285714m + m2 = 2.357142857 The m term is 1.214285714m. Take half its coefficient (0.607142857). Square it (0.3686224488) and add it to both sides. Add '0.3686224488' to each side of the equation. 1.214285714m + 0.3686224488 + m2 = 2.357142857 + 0.3686224488 Reorder the terms: 0.3686224488 + 1.214285714m + m2 = 2.357142857 + 0.3686224488 Combine like terms: 2.357142857 + 0.3686224488 = 2.7257653058 0.3686224488 + 1.214285714m + m2 = 2.7257653058 Factor a perfect square on the left side: (m + 0.607142857)(m + 0.607142857) = 2.7257653058 Calculate the square root of the right side: 1.65098919 Break this problem into two subproblems by setting (m + 0.607142857) equal to 1.65098919 and -1.65098919.Subproblem 1
m + 0.607142857 = 1.65098919 Simplifying m + 0.607142857 = 1.65098919 Reorder the terms: 0.607142857 + m = 1.65098919 Solving 0.607142857 + m = 1.65098919 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.607142857' to each side of the equation. 0.607142857 + -0.607142857 + m = 1.65098919 + -0.607142857 Combine like terms: 0.607142857 + -0.607142857 = 0.000000000 0.000000000 + m = 1.65098919 + -0.607142857 m = 1.65098919 + -0.607142857 Combine like terms: 1.65098919 + -0.607142857 = 1.043846333 m = 1.043846333 Simplifying m = 1.043846333Subproblem 2
m + 0.607142857 = -1.65098919 Simplifying m + 0.607142857 = -1.65098919 Reorder the terms: 0.607142857 + m = -1.65098919 Solving 0.607142857 + m = -1.65098919 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.607142857' to each side of the equation. 0.607142857 + -0.607142857 + m = -1.65098919 + -0.607142857 Combine like terms: 0.607142857 + -0.607142857 = 0.000000000 0.000000000 + m = -1.65098919 + -0.607142857 m = -1.65098919 + -0.607142857 Combine like terms: -1.65098919 + -0.607142857 = -2.258132047 m = -2.258132047 Simplifying m = -2.258132047Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.043846333, -2.258132047}
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