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Simplifying 3m2 + -5m + -21 = 0 Reorder the terms: -21 + -5m + 3m2 = 0 Solving -21 + -5m + 3m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -7 + -1.666666667m + m2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -1.666666667m + 7 + m2 = 0 + 7 Reorder the terms: -7 + 7 + -1.666666667m + m2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1.666666667m + m2 = 0 + 7 -1.666666667m + m2 = 0 + 7 Combine like terms: 0 + 7 = 7 -1.666666667m + m2 = 7 The m term is -1.666666667m. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667m + 0.6944444447 + m2 = 7 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667m + m2 = 7 + 0.6944444447 Combine like terms: 7 + 0.6944444447 = 7.6944444447 0.6944444447 + -1.666666667m + m2 = 7.6944444447 Factor a perfect square on the left side: (m + -0.8333333335)(m + -0.8333333335) = 7.6944444447 Calculate the square root of the right side: 2.773886163 Break this problem into two subproblems by setting (m + -0.8333333335) equal to 2.773886163 and -2.773886163.Subproblem 1
m + -0.8333333335 = 2.773886163 Simplifying m + -0.8333333335 = 2.773886163 Reorder the terms: -0.8333333335 + m = 2.773886163 Solving -0.8333333335 + m = 2.773886163 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + m = 2.773886163 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + m = 2.773886163 + 0.8333333335 m = 2.773886163 + 0.8333333335 Combine like terms: 2.773886163 + 0.8333333335 = 3.6072194965 m = 3.6072194965 Simplifying m = 3.6072194965Subproblem 2
m + -0.8333333335 = -2.773886163 Simplifying m + -0.8333333335 = -2.773886163 Reorder the terms: -0.8333333335 + m = -2.773886163 Solving -0.8333333335 + m = -2.773886163 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + m = -2.773886163 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + m = -2.773886163 + 0.8333333335 m = -2.773886163 + 0.8333333335 Combine like terms: -2.773886163 + 0.8333333335 = -1.9405528295 m = -1.9405528295 Simplifying m = -1.9405528295Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.6072194965, -1.9405528295}
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