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Simplifying m2 + -32m + -6 = 0 Reorder the terms: -6 + -32m + m2 = 0 Solving -6 + -32m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -32m + 6 + m2 = 0 + 6 Reorder the terms: -6 + 6 + -32m + m2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -32m + m2 = 0 + 6 -32m + m2 = 0 + 6 Combine like terms: 0 + 6 = 6 -32m + m2 = 6 The m term is -32m. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32m + 256 + m2 = 6 + 256 Reorder the terms: 256 + -32m + m2 = 6 + 256 Combine like terms: 6 + 256 = 262 256 + -32m + m2 = 262 Factor a perfect square on the left side: (m + -16)(m + -16) = 262 Calculate the square root of the right side: 16.186414056 Break this problem into two subproblems by setting (m + -16) equal to 16.186414056 and -16.186414056.Subproblem 1
m + -16 = 16.186414056 Simplifying m + -16 = 16.186414056 Reorder the terms: -16 + m = 16.186414056 Solving -16 + m = 16.186414056 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + m = 16.186414056 + 16 Combine like terms: -16 + 16 = 0 0 + m = 16.186414056 + 16 m = 16.186414056 + 16 Combine like terms: 16.186414056 + 16 = 32.186414056 m = 32.186414056 Simplifying m = 32.186414056Subproblem 2
m + -16 = -16.186414056 Simplifying m + -16 = -16.186414056 Reorder the terms: -16 + m = -16.186414056 Solving -16 + m = -16.186414056 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + m = -16.186414056 + 16 Combine like terms: -16 + 16 = 0 0 + m = -16.186414056 + 16 m = -16.186414056 + 16 Combine like terms: -16.186414056 + 16 = -0.186414056 m = -0.186414056 Simplifying m = -0.186414056Solution
The solution to the problem is based on the solutions from the subproblems. m = {32.186414056, -0.186414056}
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