What are the solutions to the equation 4a^2-14a+13=2 ?

The solutions to the equation 4a^2-14a+13=2 are a=(7+sqrt(5))/4 ,a=(7-sqrt(5))/4

Find the zeros of 4a^2-14a+13=2

The zeros of 4a^2-14a+13=2 are a=(7+sqrt(5))/4 ,a=(7-sqrt(5))/4

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4 a^{2} - 14 a + 13 = 2

a = \frac{7 + 5}{4}, a = \frac{7 - 5}{4}

Decimal Notation

a = 2.30901 \dots, a = 1.19098 \dots

Solution steps

4 a^{2} - 14 a + 13 = 2

Move

2

to the left side

4 a^{2} - 14 a + 11 = 0

Solve with the quadratic formula

a_{1, 2} = \frac{- ( - 14 ) \pm ( - 14 ) ^{2} - 4 \cdot 4 \cdot 11}{2 \cdot 4}

(- 14)^{2} - 4 \cdot 4 \cdot 11 = 25

a_{1, 2} = \frac{- ( - 14 ) \pm 2 5}{2 \cdot 4}

Separate the solutions

a_{1} = \frac{- ( - 14 ) + 2 5}{2 \cdot 4}, a_{2} = \frac{- ( - 14 ) - 2 5}{2 \cdot 4}

a = \frac{- ( - 14 ) + 2 5}{2 \cdot 4} : \frac{7 + 5}{4}

a = \frac{- ( - 14 ) - 2 5}{2 \cdot 4} : \frac{7 - 5}{4}

The solutions to the quadratic equation are:

a = \frac{7 + 5}{4}, a = \frac{7 - 5}{4}

2 x^{2} + 14 x + 11 = 0

x^{2} - 6 x - 31 = 0

0 = 2 x^{2} - 2 x - 5

- 4 x^{2} - 13 x - 3 = 0

x^{2} - 2 - 48 = 0

What are the solutions to the equation 4a^2-14a+13=2 ?
The solutions to the equation 4a^2-14a+13=2 are a=(7+sqrt(5))/4 ,a=(7-sqrt(5))/4
Find the zeros of 4a^2-14a+13=2
The zeros of 4a^2-14a+13=2 are a=(7+sqrt(5))/4 ,a=(7-sqrt(5))/4