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Simplifying m2 + 2m + -63 = -6 Reorder the terms: -63 + 2m + m2 = -6 Solving -63 + 2m + m2 = -6 Solving for variable 'm'. Reorder the terms: -63 + 6 + 2m + m2 = -6 + 6 Combine like terms: -63 + 6 = -57 -57 + 2m + m2 = -6 + 6 Combine like terms: -6 + 6 = 0 -57 + 2m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '57' to each side of the equation. -57 + 2m + 57 + m2 = 0 + 57 Reorder the terms: -57 + 57 + 2m + m2 = 0 + 57 Combine like terms: -57 + 57 = 0 0 + 2m + m2 = 0 + 57 2m + m2 = 0 + 57 Combine like terms: 0 + 57 = 57 2m + m2 = 57 The m term is 2m. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2m + 1 + m2 = 57 + 1 Reorder the terms: 1 + 2m + m2 = 57 + 1 Combine like terms: 57 + 1 = 58 1 + 2m + m2 = 58 Factor a perfect square on the left side: (m + 1)(m + 1) = 58 Calculate the square root of the right side: 7.615773106 Break this problem into two subproblems by setting (m + 1) equal to 7.615773106 and -7.615773106.Subproblem 1
m + 1 = 7.615773106 Simplifying m + 1 = 7.615773106 Reorder the terms: 1 + m = 7.615773106 Solving 1 + m = 7.615773106 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + m = 7.615773106 + -1 Combine like terms: 1 + -1 = 0 0 + m = 7.615773106 + -1 m = 7.615773106 + -1 Combine like terms: 7.615773106 + -1 = 6.615773106 m = 6.615773106 Simplifying m = 6.615773106Subproblem 2
m + 1 = -7.615773106 Simplifying m + 1 = -7.615773106 Reorder the terms: 1 + m = -7.615773106 Solving 1 + m = -7.615773106 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + m = -7.615773106 + -1 Combine like terms: 1 + -1 = 0 0 + m = -7.615773106 + -1 m = -7.615773106 + -1 Combine like terms: -7.615773106 + -1 = -8.615773106 m = -8.615773106 Simplifying m = -8.615773106Solution
The solution to the problem is based on the solutions from the subproblems. m = {6.615773106, -8.615773106}
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