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If x^(2)+6x-5=0, what are the values of x ? Choose 1 answer: (A) -3-sqrt14 and -3+sqrt14 (B) 3-sqrt14 and 3+sqrt14 (c) -1 and -5 (D) 1 and 5

If x2+6x−5=0 x^{2}+6 x-5=0 , what are the values of x x ?\newlineChoose 11 answer:\newline(A) −3−14 -3-\sqrt{14} and −3+14 -3+\sqrt{14} \newline(B) 3−14 3-\sqrt{14} and 3+14 3+\sqrt{14} \newline(C) −1-1 and −5-5\newline(D) 11 and 55

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Full solution

Q. If x2+6x−5=0 x^{2}+6 x-5=0 , what are the values of x x ?\newlineChoose 11 answer:\newline(A) −3−14 -3-\sqrt{14} and −3+14 -3+\sqrt{14} \newline(B) 3−14 3-\sqrt{14} and 3+14 3+\sqrt{14} \newline(C) −1-1 and −5-5\newline(D) 11 and 55
  1. Identify equation type: Identify the type of equation.\newlineThe given equation x2+6x−5=0x^2 + 6x - 5 = 0 is a quadratic equation in the standard form ax2+bx+c=0ax^2 + bx + c = 0, where a=1a = 1, b=6b = 6, and c=−5c = -5.
  2. Apply quadratic formula: Apply the quadratic formula to find the values of x.\newlineThe quadratic formula is x=−b±b2−4ac2ax = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}. For our equation, a=1a = 1, b=6b = 6, and c=−5c = -5.
  3. Calculate discriminant: Calculate the discriminant b2−4acb^2 - 4ac.\newlineDiscriminant = b2−4ac=(6)2−4(1)(−5)=36+20=56b^2 - 4ac = (6)^2 - 4(1)(-5) = 36 + 20 = 56.
  4. Calculate possible values for x: Calculate the two possible values for x using the quadratic formula.\newlinex=−6±56(2⋅1)x = \frac{{-6 \pm \sqrt{56}}}{{(2 \cdot 1)}}\newlinex=−6±4⋅142x = \frac{{-6 \pm \sqrt{4 \cdot 14}}}{{2}}\newlinex=−6±2142x = \frac{{-6 \pm 2\sqrt{14}}}{{2}}\newlinex=−3±14x = -3 \pm \sqrt{14}
  5. Write down solutions for x: Write down the two solutions for x.\newlineThe two solutions are:\newlinex = −3−14-3 - \sqrt{14}\newlinex = −3+14-3 + \sqrt{14}

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