What are the solutions to the equation 25z^2+97=100z ?

The solutions to the equation 25z^2+97=100z are z=(10+sqrt(3))/5 ,z=(10-sqrt(3))/5

Find the zeros of 25z^2+97=100z

The zeros of 25z^2+97=100z are z=(10+sqrt(3))/5 ,z=(10-sqrt(3))/5

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25 z^{2} + 97 = 100 z

z = \frac{10 + 3}{5}, z = \frac{10 - 3}{5}

Decimal Notation

z = 2.34641 \dots, z = 1.65358 \dots

Solution steps

25 z^{2} + 97 = 100 z

Move

100 z

to the left side

25 z^{2} + 97 - 100 z = 0

Write in the standard form

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

25 z^{2} - 100 z + 97 = 0

Solve with the quadratic formula

z_{1, 2} = \frac{- ( - 100 ) \pm ( - 100 ) ^{2} - 4 \cdot 25 \cdot 97}{2 \cdot 25}

(- 100)^{2} - 4 \cdot 25 \cdot 97 = 103

z_{1, 2} = \frac{- ( - 100 ) \pm 10 3}{2 \cdot 25}

Separate the solutions

z_{1} = \frac{- ( - 100 ) + 10 3}{2 \cdot 25}, z_{2} = \frac{- ( - 100 ) - 10 3}{2 \cdot 25}

z = \frac{- ( - 100 ) + 10 3}{2 \cdot 25} : \frac{10 + 3}{5}

z = \frac{- ( - 100 ) - 10 3}{2 \cdot 25} : \frac{10 - 3}{5}

The solutions to the quadratic equation are:

z = \frac{10 + 3}{5}, z = \frac{10 - 3}{5}

∣ x ∣ - 15 < - 7

- 5 (2 x - 9) = 2 (x - 8) - 11

(23 - 2)^{2}

x^{2} + 13 x + 40

X^{2} + 4 X + 3 = 0

What are the solutions to the equation 25z^2+97=100z ?
The solutions to the equation 25z^2+97=100z are z=(10+sqrt(3))/5 ,z=(10-sqrt(3))/5
Find the zeros of 25z^2+97=100z
The zeros of 25z^2+97=100z are z=(10+sqrt(3))/5 ,z=(10-sqrt(3))/5