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

2 x^{2} + 16 x - 11

x^{2} + \frac{1}{4} = 1

2 x^{2} + 6 x + 3

11 m^{2} - 11 m + 3 = 6 m^{2}

x, (x + y)^{2} = 2 x + 2 y

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)