What are the solutions to the equation 4x^2-168x+36=0 ?

The solutions to the equation 4x^2-168x+36=0 are x=3(7+4sqrt(3)),x=3(7-4sqrt(3))

Find the zeros of 4x^2-168x+36=0

The zeros of 4x^2-168x+36=0 are x=3(7+4sqrt(3)),x=3(7-4sqrt(3))

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4 x^{2} - 168 x + 36 = 0

x = 3 (7 + 43), x = 3 (7 - 43)

Decimal Notation

x = 41.78460 \dots, x = 0.21539 \dots

Solution steps

4 x^{2} - 168 x + 36 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 168 ) \pm ( - 168 ) ^{2} - 4 \cdot 4 \cdot 36}{2 \cdot 4}

(- 168)^{2} - 4 \cdot 4 \cdot 36 = 963

x_{1, 2} = \frac{- ( - 168 ) \pm 96 3}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- ( - 168 ) + 96 3}{2 \cdot 4}, x_{2} = \frac{- ( - 168 ) - 96 3}{2 \cdot 4}

x = \frac{- ( - 168 ) + 96 3}{2 \cdot 4} : 3 (7 + 43)

x = \frac{- ( - 168 ) - 96 3}{2 \cdot 4} : 3 (7 - 43)

The solutions to the quadratic equation are:

x = 3 (7 + 43), x = 3 (7 - 43)

r (r - 10) = 0

- 0.01 x^{2} + 0.04 x < x + 3

(3 x - 3)^{2} = 23

12 = - 4 (- 6 x - 3)

What are the solutions to the equation 4x^2-168x+36=0 ?
The solutions to the equation 4x^2-168x+36=0 are x=3(7+4sqrt(3)),x=3(7-4sqrt(3))
Find the zeros of 4x^2-168x+36=0
The zeros of 4x^2-168x+36=0 are x=3(7+4sqrt(3)),x=3(7-4sqrt(3))