What are the solutions to the equation 1/4 x^2-1/2 x=1 ?

The solutions to the equation 1/4 x^2-1/2 x=1 are x=1+sqrt(5),x=1-sqrt(5)

Find the zeros of 1/4 x^2-1/2 x=1

The zeros of 1/4 x^2-1/2 x=1 are x=1+sqrt(5),x=1-sqrt(5)

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\frac{1}{4} x^{2} - \frac{1}{2} x = 1

x = 1 + 5, x = 1 - 5

Decimal Notation

x = 3.23606 \dots, x = - 1.23606 \dots

Solution steps

\frac{1}{4} x^{2} - \frac{1}{2} x = 1

Find Least Common Multiplier of

4, 2 : 4

Multiply by LCM=

4

\frac{1}{4} x^{2} \cdot 4 - \frac{1}{2} x \cdot 4 = 1 \cdot 4

Simplify

x^{2} - 2 x = 4

Move

4

to the left side

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

Solve with the quadratic formula

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

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

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

x = 1 + 5, x = 1 - 5

25 x^{2} + 20 x = 6

5 x^{2} - 14 x - 3

(12 + 4 i) - (3 - 7 i)

(3 + 5) (3 - 5)

9 x = 120

What are the solutions to the equation 1/4 x^2-1/2 x=1 ?
The solutions to the equation 1/4 x^2-1/2 x=1 are x=1+sqrt(5),x=1-sqrt(5)
Find the zeros of 1/4 x^2-1/2 x=1
The zeros of 1/4 x^2-1/2 x=1 are x=1+sqrt(5),x=1-sqrt(5)