What are the solutions to the equation 45= 1/2 x(4x-2) ?

The solutions to the equation 45= 1/2 x(4x-2) are x=5,x=-9/2

Find the zeros of 45= 1/2 x(4x-2)

The zeros of 45= 1/2 x(4x-2) are x=5,x=-9/2

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45 = \frac{1}{2} x (4 x - 2)

x = 5, x = - \frac{9}{2}

Solution steps

45 = \frac{1}{2} x (4 x - 2)

Multiply both sides by

2

90 = x (4 x - 2)

Expand

x (4 x - 2) : 4 x^{2} - 2 x

90 = 4 x^{2} - 2 x

Switch sides

4 x^{2} - 2 x = 90

Move

90

to the left side

4 x^{2} - 2 x - 90 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 2 ) \pm ( - 2 ) ^{2} - 4 \cdot 4 ( - 90 )}{2 \cdot 4}

(- 2)^{2} - 4 \cdot 4 (- 90) = 38

x_{1, 2} = \frac{- ( - 2 ) \pm 38}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- ( - 2 ) + 38}{2 \cdot 4}, x_{2} = \frac{- ( - 2 ) - 38}{2 \cdot 4}

x = \frac{- ( - 2 ) + 38}{2 \cdot 4} : 5

x = \frac{- ( - 2 ) - 38}{2 \cdot 4} : - \frac{9}{2}

The solutions to the quadratic equation are:

x = 5, x = - \frac{9}{2}

\frac{x}{4} + 9 = 7

(4 - 5 i) (4 + i)

π \cdot 5^{2} \cdot \frac{3}{3}

\frac{x}{7} \geq - 6

\frac{x + 1}{2} \geq 1

What are the solutions to the equation 45= 1/2 x(4x-2) ?
The solutions to the equation 45= 1/2 x(4x-2) are x=5,x=-9/2
Find the zeros of 45= 1/2 x(4x-2)
The zeros of 45= 1/2 x(4x-2) are x=5,x=-9/2