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Simplifying 4m2 + 28m + -60 = 0 Reorder the terms: -60 + 28m + 4m2 = 0 Solving -60 + 28m + 4m2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '4'. 4(-15 + 7m + m2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-15 + 7m + m2)' equal to zero and attempt to solve: Simplifying -15 + 7m + m2 = 0 Solving -15 + 7m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 7m + 15 + m2 = 0 + 15 Reorder the terms: -15 + 15 + 7m + m2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 7m + m2 = 0 + 15 7m + m2 = 0 + 15 Combine like terms: 0 + 15 = 15 7m + m2 = 15 The m term is 7m. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7m + 12.25 + m2 = 15 + 12.25 Reorder the terms: 12.25 + 7m + m2 = 15 + 12.25 Combine like terms: 15 + 12.25 = 27.25 12.25 + 7m + m2 = 27.25 Factor a perfect square on the left side: (m + 3.5)(m + 3.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (m + 3.5) equal to 5.220153254 and -5.220153254.Subproblem 1
m + 3.5 = 5.220153254 Simplifying m + 3.5 = 5.220153254 Reorder the terms: 3.5 + m = 5.220153254 Solving 3.5 + m = 5.220153254 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + m = 5.220153254 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + m = 5.220153254 + -3.5 m = 5.220153254 + -3.5 Combine like terms: 5.220153254 + -3.5 = 1.720153254 m = 1.720153254 Simplifying m = 1.720153254Subproblem 2
m + 3.5 = -5.220153254 Simplifying m + 3.5 = -5.220153254 Reorder the terms: 3.5 + m = -5.220153254 Solving 3.5 + m = -5.220153254 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + m = -5.220153254 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + m = -5.220153254 + -3.5 m = -5.220153254 + -3.5 Combine like terms: -5.220153254 + -3.5 = -8.720153254 m = -8.720153254 Simplifying m = -8.720153254Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.720153254, -8.720153254}Solution
m = {1.720153254, -8.720153254}
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