QuestionAugust 27, 2025

Using the quadratic formula to solve 11x^2-4x=1 , what are the values of x? (2)/(11)pm (sqrt (15))/(11) (2)/(11)pm (2sqrt (15))/(11) (2)/(11)pm (sqrt (7))/(11) (2)/(11)pm (sqrt (7)i)/(11)

Using the quadratic formula to solve 11x^2-4x=1 , what are the values of x? (2)/(11)pm (sqrt (15))/(11) (2)/(11)pm (2sqrt (15))/(11) (2)/(11)pm (sqrt (7))/(11) (2)/(11)pm (sqrt (7)i)/(11)
Using the quadratic formula to solve 11x^2-4x=1 , what are the values of x?
(2)/(11)pm (sqrt (15))/(11)
(2)/(11)pm (2sqrt (15))/(11)
(2)/(11)pm (sqrt (7))/(11)
(2)/(11)pm (sqrt (7)i)/(11)

Solution
4.1(181 votes)

Answer

\frac {2}{11}\pm \frac {2\sqrt {15}}{11} Explanation 1. Write the equation in standard form 11x^2 - 4x - 1 = 0 2. Identify coefficients a = 11, b = -4, c = -1 3. Apply the quadratic formula **x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}** 4. Calculate discriminant b^2 - 4ac = (-4)^2 - 4(11)(-1) = 16 + 44 = 60 5. Substitute values into the quadratic formula x = \frac{-(-4) \pm \sqrt{60}}{2(11)} = \frac{4 \pm \sqrt{60}}{22} 6. Simplify the square root and fraction \sqrt{60} = \sqrt{4 \times 15} = 2\sqrt{15} x = \frac{4 \pm 2\sqrt{15}}{22} = \frac{2}{11} \pm \frac{2\sqrt{15}}{11}

Explanation

1. Write the equation in standard form<br /> $11x^2 - 4x - 1 = 0$<br />2. Identify coefficients<br /> $a = 11$, $b = -4$, $c = -1$<br />3. Apply the quadratic formula<br /> **$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$**<br />4. Calculate discriminant<br /> $b^2 - 4ac = (-4)^2 - 4(11)(-1) = 16 + 44 = 60$<br />5. Substitute values into the quadratic formula<br /> $x = \frac{-(-4) \pm \sqrt{60}}{2(11)} = \frac{4 \pm \sqrt{60}}{22}$<br />6. Simplify the square root and fraction<br /> $\sqrt{60} = \sqrt{4 \times 15} = 2\sqrt{15}$<br /> $x = \frac{4 \pm 2\sqrt{15}}{22} = \frac{2}{11} \pm \frac{2\sqrt{15}}{11}$
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