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Simplifying 61m2 + 7m + -3 = 0 Reorder the terms: -3 + 7m + 61m2 = 0 Solving -3 + 7m + 61m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 61 the coefficient of the squared term: Divide each side by '61'. -0.04918032787 + 0.1147540984m + m2 = 0 Move the constant term to the right: Add '0.04918032787' to each side of the equation. -0.04918032787 + 0.1147540984m + 0.04918032787 + m2 = 0 + 0.04918032787 Reorder the terms: -0.04918032787 + 0.04918032787 + 0.1147540984m + m2 = 0 + 0.04918032787 Combine like terms: -0.04918032787 + 0.04918032787 = 0.00000000000 0.00000000000 + 0.1147540984m + m2 = 0 + 0.04918032787 0.1147540984m + m2 = 0 + 0.04918032787 Combine like terms: 0 + 0.04918032787 = 0.04918032787 0.1147540984m + m2 = 0.04918032787 The m term is 0.1147540984m. Take half its coefficient (0.0573770492). Square it (0.003292125775) and add it to both sides. Add '0.003292125775' to each side of the equation. 0.1147540984m + 0.003292125775 + m2 = 0.04918032787 + 0.003292125775 Reorder the terms: 0.003292125775 + 0.1147540984m + m2 = 0.04918032787 + 0.003292125775 Combine like terms: 0.04918032787 + 0.003292125775 = 0.052472453645 0.003292125775 + 0.1147540984m + m2 = 0.052472453645 Factor a perfect square on the left side: (m + 0.0573770492)(m + 0.0573770492) = 0.052472453645 Calculate the square root of the right side: 0.229068666 Break this problem into two subproblems by setting (m + 0.0573770492) equal to 0.229068666 and -0.229068666.Subproblem 1
m + 0.0573770492 = 0.229068666 Simplifying m + 0.0573770492 = 0.229068666 Reorder the terms: 0.0573770492 + m = 0.229068666 Solving 0.0573770492 + m = 0.229068666 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.0573770492' to each side of the equation. 0.0573770492 + -0.0573770492 + m = 0.229068666 + -0.0573770492 Combine like terms: 0.0573770492 + -0.0573770492 = 0.0000000000 0.0000000000 + m = 0.229068666 + -0.0573770492 m = 0.229068666 + -0.0573770492 Combine like terms: 0.229068666 + -0.0573770492 = 0.1716916168 m = 0.1716916168 Simplifying m = 0.1716916168Subproblem 2
m + 0.0573770492 = -0.229068666 Simplifying m + 0.0573770492 = -0.229068666 Reorder the terms: 0.0573770492 + m = -0.229068666 Solving 0.0573770492 + m = -0.229068666 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.0573770492' to each side of the equation. 0.0573770492 + -0.0573770492 + m = -0.229068666 + -0.0573770492 Combine like terms: 0.0573770492 + -0.0573770492 = 0.0000000000 0.0000000000 + m = -0.229068666 + -0.0573770492 m = -0.229068666 + -0.0573770492 Combine like terms: -0.229068666 + -0.0573770492 = -0.2864457152 m = -0.2864457152 Simplifying m = -0.2864457152Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.1716916168, -0.2864457152}
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