What are the solutions to the equation 7=x(x-4) ?

The solutions to the equation 7=x(x-4) are x=2+sqrt(11),x=2-sqrt(11)

Find the zeros of 7=x(x-4)

The zeros of 7=x(x-4) are x=2+sqrt(11),x=2-sqrt(11)

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7 = x (x - 4)

x = 2 + 11, x = 2 - 11

Decimal Notation

x = 5.31662 \dots, x = - 1.31662 \dots

Solution steps

7 = x (x - 4)

Expand

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

7 = x^{2} - 4 x

Switch sides

x^{2} - 4 x = 7

Move

7

to the left side

x^{2} - 4 x - 7 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 4 ) \pm ( - 4 ) ^{2} - 4 \cdot 1 \cdot ( - 7 )}{2 \cdot 1}

(- 4)^{2} - 4 \cdot 1 \cdot (- 7) = 211

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

Separate the solutions

x_{1} = \frac{- ( - 4 ) + 2 11}{2 \cdot 1}, x_{2} = \frac{- ( - 4 ) - 2 11}{2 \cdot 1}

x = \frac{- ( - 4 ) + 2 11}{2 \cdot 1} : 2 + 11

x = \frac{- ( - 4 ) - 2 11}{2 \cdot 1} : 2 - 11

The solutions to the quadratic equation are:

x = 2 + 11, x = 2 - 11

15 x^{2} - 4 x - 126 = - 30

\frac{k ^{2}}{1.2 - 7} = 23

x^{2} - 4 + 3 = 0

6 x^{2} - 2 x = 20

0 = x^{2} + 9

What are the solutions to the equation 7=x(x-4) ?
The solutions to the equation 7=x(x-4) are x=2+sqrt(11),x=2-sqrt(11)
Find the zeros of 7=x(x-4)
The zeros of 7=x(x-4) are x=2+sqrt(11),x=2-sqrt(11)