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Simplifying 9m2 + -8m + 1 = 0 Reorder the terms: 1 + -8m + 9m2 = 0 Solving 1 + -8m + 9m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.1111111111 + -0.8888888889m + m2 = 0 Move the constant term to the right: Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.8888888889m + -0.1111111111 + m2 = 0 + -0.1111111111 Reorder the terms: 0.1111111111 + -0.1111111111 + -0.8888888889m + m2 = 0 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + -0.8888888889m + m2 = 0 + -0.1111111111 -0.8888888889m + m2 = 0 + -0.1111111111 Combine like terms: 0 + -0.1111111111 = -0.1111111111 -0.8888888889m + m2 = -0.1111111111 The m term is -0.8888888889m. Take half its coefficient (-0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. -0.8888888889m + 0.1975308642 + m2 = -0.1111111111 + 0.1975308642 Reorder the terms: 0.1975308642 + -0.8888888889m + m2 = -0.1111111111 + 0.1975308642 Combine like terms: -0.1111111111 + 0.1975308642 = 0.0864197531 0.1975308642 + -0.8888888889m + m2 = 0.0864197531 Factor a perfect square on the left side: (m + -0.4444444445)(m + -0.4444444445) = 0.0864197531 Calculate the square root of the right side: 0.293972368 Break this problem into two subproblems by setting (m + -0.4444444445) equal to 0.293972368 and -0.293972368.Subproblem 1
m + -0.4444444445 = 0.293972368 Simplifying m + -0.4444444445 = 0.293972368 Reorder the terms: -0.4444444445 + m = 0.293972368 Solving -0.4444444445 + m = 0.293972368 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + m = 0.293972368 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + m = 0.293972368 + 0.4444444445 m = 0.293972368 + 0.4444444445 Combine like terms: 0.293972368 + 0.4444444445 = 0.7384168125 m = 0.7384168125 Simplifying m = 0.7384168125Subproblem 2
m + -0.4444444445 = -0.293972368 Simplifying m + -0.4444444445 = -0.293972368 Reorder the terms: -0.4444444445 + m = -0.293972368 Solving -0.4444444445 + m = -0.293972368 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + m = -0.293972368 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + m = -0.293972368 + 0.4444444445 m = -0.293972368 + 0.4444444445 Combine like terms: -0.293972368 + 0.4444444445 = 0.1504720765 m = 0.1504720765 Simplifying m = 0.1504720765Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.7384168125, 0.1504720765}
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