What are the solutions to the equation quadraticformula x^2=3x-1 ?

The solutions to the equation quadraticformula x^2=3x-1 are x=(3+sqrt(5))/2 ,x=(3-sqrt(5))/2

Find the zeros of quadraticformula x^2=3x-1

The zeros of quadraticformula x^2=3x-1 are x=(3+sqrt(5))/2 ,x=(3-sqrt(5))/2

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x^{2} = 3 x - 1

x = \frac{3 + 5}{2}, x = \frac{3 - 5}{2}

Decimal Notation

x = 2.61803 \dots, x = 0.38196 \dots

Solution steps

x^{2} = 3 x - 1

Move

1

to the left side

x^{2} + 1 = 3 x

Move

3 x

to the left side

x^{2} + 1 - 3 x = 0

Write in the standard form

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

x^{2} - 3 x + 1 = 0

Solve with the quadratic formula

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

(- 3)^{2} - 4 \cdot 1 \cdot 1 = 5

x_{1, 2} = \frac{- ( - 3 ) \pm 5}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 3 ) + 5}{2 \cdot 1}, x_{2} = \frac{- ( - 3 ) - 5}{2 \cdot 1}

x = \frac{- ( - 3 ) + 5}{2 \cdot 1} : \frac{3 + 5}{2}

x = \frac{- ( - 3 ) - 5}{2 \cdot 1} : \frac{3 - 5}{2}

The solutions to the quadratic equation are:

x = \frac{3 + 5}{2}, x = \frac{3 - 5}{2}

w, \frac{( 2 w - 1 )}{4} = 2 - w

x, 2 - (2 x - 5) = 2 (x + 5) - 2

x^{2} - 12 x = - 35

4 \frac{1}{2} \cdot 2 \frac{1}{4}

x, 7 - 2 x = - 3

What are the solutions to the equation quadraticformula x^2=3x-1 ?
The solutions to the equation quadraticformula x^2=3x-1 are x=(3+sqrt(5))/2 ,x=(3-sqrt(5))/2
Find the zeros of quadraticformula x^2=3x-1
The zeros of quadraticformula x^2=3x-1 are x=(3+sqrt(5))/2 ,x=(3-sqrt(5))/2