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Simplifying 32m2 + 11m + -6 = 0 Reorder the terms: -6 + 11m + 32m2 = 0 Solving -6 + 11m + 32m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -0.1875 + 0.34375m + m2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + 0.34375m + 0.1875 + m2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + 0.34375m + m2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + 0.34375m + m2 = 0 + 0.1875 0.34375m + m2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 0.34375m + m2 = 0.1875 The m term is 0.34375m. Take half its coefficient (0.171875). Square it (0.02954101563) and add it to both sides. Add '0.02954101563' to each side of the equation. 0.34375m + 0.02954101563 + m2 = 0.1875 + 0.02954101563 Reorder the terms: 0.02954101563 + 0.34375m + m2 = 0.1875 + 0.02954101563 Combine like terms: 0.1875 + 0.02954101563 = 0.21704101563 0.02954101563 + 0.34375m + m2 = 0.21704101563 Factor a perfect square on the left side: (m + 0.171875)(m + 0.171875) = 0.21704101563 Calculate the square root of the right side: 0.46587661 Break this problem into two subproblems by setting (m + 0.171875) equal to 0.46587661 and -0.46587661.Subproblem 1
m + 0.171875 = 0.46587661 Simplifying m + 0.171875 = 0.46587661 Reorder the terms: 0.171875 + m = 0.46587661 Solving 0.171875 + m = 0.46587661 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.171875' to each side of the equation. 0.171875 + -0.171875 + m = 0.46587661 + -0.171875 Combine like terms: 0.171875 + -0.171875 = 0.000000 0.000000 + m = 0.46587661 + -0.171875 m = 0.46587661 + -0.171875 Combine like terms: 0.46587661 + -0.171875 = 0.29400161 m = 0.29400161 Simplifying m = 0.29400161Subproblem 2
m + 0.171875 = -0.46587661 Simplifying m + 0.171875 = -0.46587661 Reorder the terms: 0.171875 + m = -0.46587661 Solving 0.171875 + m = -0.46587661 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.171875' to each side of the equation. 0.171875 + -0.171875 + m = -0.46587661 + -0.171875 Combine like terms: 0.171875 + -0.171875 = 0.000000 0.000000 + m = -0.46587661 + -0.171875 m = -0.46587661 + -0.171875 Combine like terms: -0.46587661 + -0.171875 = -0.63775161 m = -0.63775161 Simplifying m = -0.63775161Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.29400161, -0.63775161}
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