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Simplifying 3m2 + 30m + -75 = 0 Reorder the terms: -75 + 30m + 3m2 = 0 Solving -75 + 30m + 3m2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '3'. 3(-25 + 10m + m2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-25 + 10m + m2)' equal to zero and attempt to solve: Simplifying -25 + 10m + m2 = 0 Solving -25 + 10m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 10m + 25 + m2 = 0 + 25 Reorder the terms: -25 + 25 + 10m + m2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 10m + m2 = 0 + 25 10m + m2 = 0 + 25 Combine like terms: 0 + 25 = 25 10m + m2 = 25 The m term is 10m. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10m + 25 + m2 = 25 + 25 Reorder the terms: 25 + 10m + m2 = 25 + 25 Combine like terms: 25 + 25 = 50 25 + 10m + m2 = 50 Factor a perfect square on the left side: (m + 5)(m + 5) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (m + 5) equal to 7.071067812 and -7.071067812.Subproblem 1
m + 5 = 7.071067812 Simplifying m + 5 = 7.071067812 Reorder the terms: 5 + m = 7.071067812 Solving 5 + m = 7.071067812 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + m = 7.071067812 + -5 Combine like terms: 5 + -5 = 0 0 + m = 7.071067812 + -5 m = 7.071067812 + -5 Combine like terms: 7.071067812 + -5 = 2.071067812 m = 2.071067812 Simplifying m = 2.071067812Subproblem 2
m + 5 = -7.071067812 Simplifying m + 5 = -7.071067812 Reorder the terms: 5 + m = -7.071067812 Solving 5 + m = -7.071067812 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + m = -7.071067812 + -5 Combine like terms: 5 + -5 = 0 0 + m = -7.071067812 + -5 m = -7.071067812 + -5 Combine like terms: -7.071067812 + -5 = -12.071067812 m = -12.071067812 Simplifying m = -12.071067812Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.071067812, -12.071067812}Solution
m = {2.071067812, -12.071067812}
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