What are the solutions to the equation (a-1)^2=5a ?

The solutions to the equation (a-1)^2=5a are a=(7+3sqrt(5))/2 ,a=(7-3sqrt(5))/2

Find the zeros of (a-1)^2=5a

The zeros of (a-1)^2=5a are a=(7+3sqrt(5))/2 ,a=(7-3sqrt(5))/2

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(a - 1)^{2} = 5 a

a = \frac{7 + 3 5}{2}, a = \frac{7 - 3 5}{2}

Decimal

a = 6.85410 \dots, a = 0.14589 \dots

Solution steps

(a - 1)^{2} = 5 a

Expand

(a - 1)^{2} : a^{2} - 2 a + 1

a^{2} - 2 a + 1 = 5 a

Move

5 a

to the left side

a^{2} - 7 a + 1 = 0

Solve with the quadratic formula

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

(- 7)^{2} - 4 \cdot 1 \cdot 1 = 35

a_{1, 2} = \frac{- ( - 7 ) \pm 3 5}{2 \cdot 1}

Separate the solutions

a_{1} = \frac{- ( - 7 ) + 3 5}{2 \cdot 1}, a_{2} = \frac{- ( - 7 ) - 3 5}{2 \cdot 1}

a = \frac{- ( - 7 ) + 3 5}{2 \cdot 1} : \frac{7 + 3 5}{2}

a = \frac{- ( - 7 ) - 3 5}{2 \cdot 1} : \frac{7 - 3 5}{2}

The solutions to the quadratic equation are:

a = \frac{7 + 3 5}{2}, a = \frac{7 - 3 5}{2}

15 x^{2} - 4 = 0

(2 x - 3)^{2} + 7 = 0

x^{2} - 1 = - 3

10 x^{2} - 5 x - 30 = 0

0 = 100 + 87 t - 5 t^{2}

What are the solutions to the equation (a-1)^2=5a ?
The solutions to the equation (a-1)^2=5a are a=(7+3sqrt(5))/2 ,a=(7-3sqrt(5))/2
Find the zeros of (a-1)^2=5a
The zeros of (a-1)^2=5a are a=(7+3sqrt(5))/2 ,a=(7-3sqrt(5))/2