What are the solutions to the equation 5(x^2-1)=(3x-2)^2 ?

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

Find the zeros of 5(x^2-1)=(3x-2)^2

The zeros of 5(x^2-1)=(3x-2)^2 are x= 3/2

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5 (x^{2} - 1) = (3 x - 2)^{2}

x = \frac{3}{2}

Decimal Notation

x = 1.5

Solution steps

5 (x^{2} - 1) = (3 x - 2)^{2}

Expand

5 (x^{2} - 1) : 5 x^{2} - 5

Expand

(3 x - 2)^{2} : 9 x^{2} - 12 x + 4

5 x^{2} - 5 = 9 x^{2} - 12 x + 4

Switch sides

9 x^{2} - 12 x + 4 = 5 x^{2} - 5

Move

5

to the left side

9 x^{2} - 12 x + 9 = 5 x^{2}

Move

5 x^{2}

to the left side

4 x^{2} - 12 x + 9 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 12 ) \pm ( - 12 ) ^{2} - 4 \cdot 4 \cdot 9}{2 \cdot 4}

(- 12)^{2} - 4 \cdot 4 \cdot 9 = 0

x_{1, 2} = \frac{- ( - 12 ) \pm 0}{2 \cdot 4}

x = \frac{- ( - 12 )}{2 \cdot 4}

\frac{- ( - 12 )}{2 \cdot 4} = \frac{3}{2}

x = \frac{3}{2}

The solution to the quadratic equation is:

x = \frac{3}{2}

5 x^{2} + 3 = 16 x

4 x^{2} + 20 x + 16 = 0

t, s = - 16 t^{2} + 96 t

y^{2} + 5 y + 5 = 0

x^{2} - 8 x - 76 = 8

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