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

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

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

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

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x (2 x - 3) = - 1

x = 1, x = \frac{1}{2}

Decimal Notation

x = 1, x = 0.5

Solution steps

x (2 x - 3) = - 1

Expand

x (2 x - 3) : 2 x^{2} - 3 x

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

Move

1

to the left side

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

Solve with the quadratic formula

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

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

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

x = 1, x = \frac{1}{2}

2 x^{2} - 4 x + 3 = 0

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

42 = x^{2} + x

x^{2} + 12 x + 64 = 0

a^{2} = 7 a + 60

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