What are the solutions to the equation x^2+11=8x ?

The solutions to the equation x^2+11=8x are x=4+sqrt(5),x=4-sqrt(5)

Find the zeros of x^2+11=8x

The zeros of x^2+11=8x are x=4+sqrt(5),x=4-sqrt(5)

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x^{2} + 11 = 8 x

x = 4 + 5, x = 4 - 5

Decimal Notation

x = 6.23606 \dots, x = 1.76393 \dots

Solution steps

x^{2} + 11 = 8 x

Move

8 x

to the left side

x^{2} + 11 - 8 x = 0

Write in the standard form

a x^{2} + b x + c = 0

x^{2} - 8 x + 11 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 8 ) \pm ( - 8 ) ^{2} - 4 \cdot 1 \cdot 11}{2 \cdot 1}

(- 8)^{2} - 4 \cdot 1 \cdot 11 = 25

x_{1, 2} = \frac{- ( - 8 ) \pm 2 5}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 8 ) + 2 5}{2 \cdot 1}, x_{2} = \frac{- ( - 8 ) - 2 5}{2 \cdot 1}

x = \frac{- ( - 8 ) + 2 5}{2 \cdot 1} : 4 + 5

x = \frac{- ( - 8 ) - 2 5}{2 \cdot 1} : 4 - 5

The solutions to the quadratic equation are:

x = 4 + 5, x = 4 - 5

18 x^{2} = - 27 x

10 x^{2} - 13 x - 6 = 0

(x - 5) (x + 3) = 0

4 x^{2} + 7 x + 9 = 0

(2) - x^{(2)} = 4

What are the solutions to the equation x^2+11=8x ?
The solutions to the equation x^2+11=8x are x=4+sqrt(5),x=4-sqrt(5)
Find the zeros of x^2+11=8x
The zeros of x^2+11=8x are x=4+sqrt(5),x=4-sqrt(5)