What are the solutions to the equation x^2-14x=11 ?

The solutions to the equation x^2-14x=11 are x=7+2sqrt(15),x=7-2sqrt(15)

Find the zeros of x^2-14x=11

The zeros of x^2-14x=11 are x=7+2sqrt(15),x=7-2sqrt(15)

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x^{2} - 14 x = 11

x = 7 + 215, x = 7 - 215

Decimal Notation

x = 14.74596 \dots, x = - 0.74596 \dots

Solution steps

x^{2} - 14 x = 11

Move

11

to the left side

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

Solve with the quadratic formula

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

(- 14)^{2} - 4 \cdot 1 \cdot (- 11) = 415

x_{1, 2} = \frac{- ( - 14 ) \pm 4 15}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 14 ) + 4 15}{2 \cdot 1}, x_{2} = \frac{- ( - 14 ) - 4 15}{2 \cdot 1}

x = \frac{- ( - 14 ) + 4 15}{2 \cdot 1} : 7 + 215

x = \frac{- ( - 14 ) - 4 15}{2 \cdot 1} : 7 - 215

The solutions to the quadratic equation are:

x = 7 + 215, x = 7 - 215

6 x^{2} - 8 x + 2 = 0

x^{2} + 6 x - 1 = 0

3 b^{2} - 12 b = 15

x^{2} + 3 x - 74 = 0

x (5 x + 14) = 3

What are the solutions to the equation x^2-14x=11 ?
The solutions to the equation x^2-14x=11 are x=7+2sqrt(15),x=7-2sqrt(15)
Find the zeros of x^2-14x=11
The zeros of x^2-14x=11 are x=7+2sqrt(15),x=7-2sqrt(15)