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Simplifying 8m(m + -5) + 3 = 27 Reorder the terms: 8m(-5 + m) + 3 = 27 (-5 * 8m + m * 8m) + 3 = 27 (-40m + 8m2) + 3 = 27 Reorder the terms: 3 + -40m + 8m2 = 27 Solving 3 + -40m + 8m2 = 27 Solving for variable 'm'. Reorder the terms: 3 + -27 + -40m + 8m2 = 27 + -27 Combine like terms: 3 + -27 = -24 -24 + -40m + 8m2 = 27 + -27 Combine like terms: 27 + -27 = 0 -24 + -40m + 8m2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-3 + -5m + m2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-3 + -5m + m2)' equal to zero and attempt to solve: Simplifying -3 + -5m + m2 = 0 Solving -3 + -5m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -5m + 3 + m2 = 0 + 3 Reorder the terms: -3 + 3 + -5m + m2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5m + m2 = 0 + 3 -5m + m2 = 0 + 3 Combine like terms: 0 + 3 = 3 -5m + m2 = 3 The m term is -5m. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5m + 6.25 + m2 = 3 + 6.25 Reorder the terms: 6.25 + -5m + m2 = 3 + 6.25 Combine like terms: 3 + 6.25 = 9.25 6.25 + -5m + m2 = 9.25 Factor a perfect square on the left side: (m + -2.5)(m + -2.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (m + -2.5) equal to 3.041381265 and -3.041381265.Subproblem 1
m + -2.5 = 3.041381265 Simplifying m + -2.5 = 3.041381265 Reorder the terms: -2.5 + m = 3.041381265 Solving -2.5 + m = 3.041381265 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + m = 3.041381265 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + m = 3.041381265 + 2.5 m = 3.041381265 + 2.5 Combine like terms: 3.041381265 + 2.5 = 5.541381265 m = 5.541381265 Simplifying m = 5.541381265Subproblem 2
m + -2.5 = -3.041381265 Simplifying m + -2.5 = -3.041381265 Reorder the terms: -2.5 + m = -3.041381265 Solving -2.5 + m = -3.041381265 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + m = -3.041381265 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + m = -3.041381265 + 2.5 m = -3.041381265 + 2.5 Combine like terms: -3.041381265 + 2.5 = -0.541381265 m = -0.541381265 Simplifying m = -0.541381265Solution
The solution to the problem is based on the solutions from the subproblems. m = {5.541381265, -0.541381265}Solution
m = {5.541381265, -0.541381265}
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