QuestionDecember 26, 2025

Solve for all possible values of x. sqrt (8x+17)=x+3 Answer Attempt 1 out of 2 x=square

Solve for all possible values of x. sqrt (8x+17)=x+3 Answer Attempt 1 out of 2 x=square
Solve for all possible values of x. sqrt (8x+17)=x+3 Answer Attempt 1 out of 2 x=square

Solution
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Answer

x = 4,\ -2 Explanation 1. Isolate the square root \sqrt{8x+17} = x + 3 2. Square both sides (\sqrt{8x+17})^2 = (x+3)^2 \implies 8x+17 = x^2 + 6x + 9 3. Rearrange into a quadratic equation 8x+17 - 8x - 17 = x^2 + 6x + 9 - 8x - 17 \implies x^2 - 2x - 8 = 0 4. Factor the quadratic (x-4)(x+2) = 0 5. Solve for x x = 4 or x = -2 6. Check for extraneous solutions For x=4: \sqrt{8(4)+17}=4+3 \implies \sqrt{49}=7 (valid). For x=-2: \sqrt{8(-2)+17} = -2+3 \implies \sqrt{1}=1 (valid).

Explanation

1. Isolate the square root<br /> $\sqrt{8x+17} = x + 3$<br />2. Square both sides<br /> $(\sqrt{8x+17})^2 = (x+3)^2 \implies 8x+17 = x^2 + 6x + 9$<br />3. Rearrange into a quadratic equation<br /> $8x+17 - 8x - 17 = x^2 + 6x + 9 - 8x - 17 \implies x^2 - 2x - 8 = 0$<br />4. Factor the quadratic<br /> $(x-4)(x+2) = 0$<br />5. Solve for $x$<br /> $x = 4$ or $x = -2$<br />6. Check for extraneous solutions<br /> For $x=4$: $\sqrt{8(4)+17}=4+3 \implies \sqrt{49}=7$ (valid). <br />For $x=-2$: $\sqrt{8(-2)+17} = -2+3 \implies \sqrt{1}=1$ (valid).
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