If the roots of the quadratic equation x^{2}+ | vedclass

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Question

(B) Given the quadratic equation: $x^{2}+8x+3=0$.Step $1$: Shift the constant term to the right side: $x^{2}+8x = -3$.Step $2$: Add the square of half

Vedclass · Accepted Answer

$-4+\sqrt{13}, -4-\sqrt{13}$

Vedclass · Answer

(B) Given the quadratic equation: $x^{2}+8x+3=0$.Step $1$: Shift the constant term to the right side: $x^{2}+8x = -3$.Step $2$: Add the square of half the coefficient of $x$ to both sides. The coefficient of $x$ is $8$,so half of it is $4$,and its square is $4^{2} = 16$.$x^{2}+8x+16 = -3+16$.Step $3$: Write the left side as a perfect square: $(x+4)^{2} = 13$.Step $4$: Take the square root of both sides: $x+4 = \pm\sqrt{13}$.Step $5$: Solve for $x$: $x = -4 \pm \sqrt{13}$.Thus,the roots are $-4+\sqrt{13}$ and $-4-\sqrt{13}$.

If the roots of the quadratic equation $x^{2}+8x+3=0$ exist,find them using the method of completing the square.

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