What are the solutions to the equation 16z^2+61=64z ?

The solutions to the equation 16z^2+61=64z are z=(8+sqrt(3))/4 ,z=(8-sqrt(3))/4

Find the zeros of 16z^2+61=64z

The zeros of 16z^2+61=64z are z=(8+sqrt(3))/4 ,z=(8-sqrt(3))/4

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16 z^{2} + 61 = 64 z

z = \frac{8 + 3}{4}, z = \frac{8 - 3}{4}

Decimal Notation

z = 2.43301 \dots, z = 1.56698 \dots

Solution steps

16 z^{2} + 61 = 64 z

Move

64 z

to the left side

16 z^{2} + 61 - 64 z = 0

Write in the standard form

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

16 z^{2} - 64 z + 61 = 0

Solve with the quadratic formula

z_{1, 2} = \frac{- ( - 64 ) \pm ( - 64 ) ^{2} - 4 \cdot 16 \cdot 61}{2 \cdot 16}

(- 64)^{2} - 4 \cdot 16 \cdot 61 = 83

z_{1, 2} = \frac{- ( - 64 ) \pm 8 3}{2 \cdot 16}

Separate the solutions

z_{1} = \frac{- ( - 64 ) + 8 3}{2 \cdot 16}, z_{2} = \frac{- ( - 64 ) - 8 3}{2 \cdot 16}

z = \frac{- ( - 64 ) + 8 3}{2 \cdot 16} : \frac{8 + 3}{4}

z = \frac{- ( - 64 ) - 8 3}{2 \cdot 16} : \frac{8 - 3}{4}

The solutions to the quadratic equation are:

z = \frac{8 + 3}{4}, z = \frac{8 - 3}{4}

88 = x^{2}

5 \cdot 9

15!

∣ 3 x - 2 ∣ < 2 ∣ x - 4 ∣

x^{2} - \frac{7}{2} x + 6

What are the solutions to the equation 16z^2+61=64z ?
The solutions to the equation 16z^2+61=64z are z=(8+sqrt(3))/4 ,z=(8-sqrt(3))/4
Find the zeros of 16z^2+61=64z
The zeros of 16z^2+61=64z are z=(8+sqrt(3))/4 ,z=(8-sqrt(3))/4