What are the solutions to the equation 4X^2-32X+20=0 ?

The solutions to the equation 4X^2-32X+20=0 are X=4+sqrt(11),X=4-sqrt(11)

Find the zeros of 4X^2-32X+20=0

The zeros of 4X^2-32X+20=0 are X=4+sqrt(11),X=4-sqrt(11)

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4 X^{2} - 32 X + 20 = 0

X = 4 + 11, X = 4 - 11

Decimal Notation

X = 7.31662 \dots, X = 0.68337 \dots

Solution steps

4 X^{2} - 32 X + 20 = 0

Solve with the quadratic formula

X_{1, 2} = \frac{- ( - 32 ) \pm ( - 32 ) ^{2} - 4 \cdot 4 \cdot 20}{2 \cdot 4}

(- 32)^{2} - 4 \cdot 4 \cdot 20 = 811

X_{1, 2} = \frac{- ( - 32 ) \pm 8 11}{2 \cdot 4}

Separate the solutions

X_{1} = \frac{- ( - 32 ) + 8 11}{2 \cdot 4}, X_{2} = \frac{- ( - 32 ) - 8 11}{2 \cdot 4}

X = \frac{- ( - 32 ) + 8 11}{2 \cdot 4} : 4 + 11

X = \frac{- ( - 32 ) - 8 11}{2 \cdot 4} : 4 - 11

The solutions to the quadratic equation are:

X = 4 + 11, X = 4 - 11

14 x^{2} - 45 x - 14 = 0

- 4 x^{2} - 24 x - 28 = 0

12 x^{2} - 7 x - 1 = 0

(x) = 3 x^{2} - 6 x + 2

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

What are the solutions to the equation 4X^2-32X+20=0 ?
The solutions to the equation 4X^2-32X+20=0 are X=4+sqrt(11),X=4-sqrt(11)
Find the zeros of 4X^2-32X+20=0
The zeros of 4X^2-32X+20=0 are X=4+sqrt(11),X=4-sqrt(11)