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x2+8x+6=0x^{2}+8x+6=0\newlineWhat are the solutions to the given equation?\newlineChoose 11 answer:\newline(A) x=−8−10 and  x=−8+10x=-8-\sqrt{10} \text{ and } \ x=-8+\sqrt{10}\newline(B) x=−8−7 and  x=−8+7x=-8-\sqrt{7} \text{ and } \ x=-8+\sqrt{7}\newline(C) x=−4−10 and  x=−4+10x=-4-\sqrt{10} \text{ and } \ x=-4+\sqrt{10}\newline(D) x=−4−7 and  x=−4+7x=-4-\sqrt{7} \text{ and } \ x=-4+\sqrt{7}

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Q. x2+8x+6=0x^{2}+8x+6=0\newlineWhat are the solutions to the given equation?\newlineChoose 11 answer:\newline(A) x=−8−10 and  x=−8+10x=-8-\sqrt{10} \text{ and } \ x=-8+\sqrt{10}\newline(B) x=−8−7 and  x=−8+7x=-8-\sqrt{7} \text{ and } \ x=-8+\sqrt{7}\newline(C) x=−4−10 and  x=−4+10x=-4-\sqrt{10} \text{ and } \ x=-4+\sqrt{10}\newline(D) x=−4−7 and  x=−4+7x=-4-\sqrt{7} \text{ and } \ x=-4+\sqrt{7}
  1. Apply Quadratic Formula: Use the quadratic formula x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where a=1a = 1, b=8b = 8, and c=6c = 6.
  2. Calculate Discriminant: Calculate the discriminant: b2−4ac=82−4(1)(6)=64−24=40b^2 - 4ac = 8^2 - 4(1)(6) = 64 - 24 = 40.
  3. Find Square Root: Find the square root of the discriminant: 40=4×10=210.\sqrt{40} = \sqrt{4\times10} = 2\sqrt{10}.
  4. Plug Values: Plug the values into the quadratic formula: x=−8±2102⋅1x = \frac{{-8 \pm 2\sqrt{10}}}{{2 \cdot 1}}.
  5. Simplify Expression: Simplify the expression: x=−8±2102=−4±10x = \frac{{-8 \pm 2\sqrt{10}}}{2} = -4 \pm \sqrt{10}.

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