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Simplifying m2 + -8m + -63 = -10 Reorder the terms: -63 + -8m + m2 = -10 Solving -63 + -8m + m2 = -10 Solving for variable 'm'. Reorder the terms: -63 + 10 + -8m + m2 = -10 + 10 Combine like terms: -63 + 10 = -53 -53 + -8m + m2 = -10 + 10 Combine like terms: -10 + 10 = 0 -53 + -8m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '53' to each side of the equation. -53 + -8m + 53 + m2 = 0 + 53 Reorder the terms: -53 + 53 + -8m + m2 = 0 + 53 Combine like terms: -53 + 53 = 0 0 + -8m + m2 = 0 + 53 -8m + m2 = 0 + 53 Combine like terms: 0 + 53 = 53 -8m + m2 = 53 The m term is -8m. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8m + 16 + m2 = 53 + 16 Reorder the terms: 16 + -8m + m2 = 53 + 16 Combine like terms: 53 + 16 = 69 16 + -8m + m2 = 69 Factor a perfect square on the left side: (m + -4)(m + -4) = 69 Calculate the square root of the right side: 8.306623863 Break this problem into two subproblems by setting (m + -4) equal to 8.306623863 and -8.306623863.Subproblem 1
m + -4 = 8.306623863 Simplifying m + -4 = 8.306623863 Reorder the terms: -4 + m = 8.306623863 Solving -4 + m = 8.306623863 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + m = 8.306623863 + 4 Combine like terms: -4 + 4 = 0 0 + m = 8.306623863 + 4 m = 8.306623863 + 4 Combine like terms: 8.306623863 + 4 = 12.306623863 m = 12.306623863 Simplifying m = 12.306623863Subproblem 2
m + -4 = -8.306623863 Simplifying m + -4 = -8.306623863 Reorder the terms: -4 + m = -8.306623863 Solving -4 + m = -8.306623863 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + m = -8.306623863 + 4 Combine like terms: -4 + 4 = 0 0 + m = -8.306623863 + 4 m = -8.306623863 + 4 Combine like terms: -8.306623863 + 4 = -4.306623863 m = -4.306623863 Simplifying m = -4.306623863Solution
The solution to the problem is based on the solutions from the subproblems. m = {12.306623863, -4.306623863}
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