sqrt(41-8a)+7=a

Question

sqrt(41-8a)+7=a

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Isolate square root: Isolate the square root on one side of the equation by subtracting 7 from both sides. sqrt(41 - 8a) + 7 - 7 = a - 7 sqrt(41 - 8a) = a - 7Square both sides: Square both sides of the equation to eliminate the square root. (sqrt(41 - 8a))^2 = (a - 7)^2 41 - 8a = (a - 7)(a - 7)Expand and simplify: Expand the right side of the equation using the FOIL method (First, Outer, Inner, Last). 41 - 8a = a^2 - 7a - 7a + 49 41 - 8a = a^2 - 14a + 49Combine terms: Move all terms to one side to set the equation to zero and combine like terms. 0 = a^2 - 14a + 49 - 41 + 8a 0 = a^2 - 6a + 8Factor quadratic equation: Factor the quadratic equation. 0 = (a - 4)(a - 2)Set equal and solve: Set each factor equal to zero and solve for 'a'. a - 4 = 0 or a - 2 = 0 a = 4 or a = 2Check first solution: Check both solutions in the original equation to ensure they do not result in taking the square root of a negative number. For a = 4: sqrt(41 - 8(4)) + 7 = 4 sqrt(41 - 32) + 7 = 4 sqrt(9) + 7 = 4 3 + 7 = 4 10 ≠ 4 This solution does not work.Check second solution: Check the second solution, a = 2: sqrt(41 - 8(2)) + 7 = 2 sqrt(41 - 16) + 7 = 2 sqrt(25) + 7 = 2 5 + 7 = 2 12 ≠ 2 This solution also does not work.No valid solution: Since neither solution satisfies the original equation, there is no solution to the equation sqrt(41-8a)+7=a.

$\sqrt{41-8a}+7=a$

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41−8a+7=a\sqrt{41-8a}+7=a41−8a​+7=a

$\sqrt{41-8a}+7=a$