What are the solutions to the equation 4x^2-24x+16=0 ?

The solutions to the equation 4x^2-24x+16=0 are x=3+sqrt(5),x=3-sqrt(5)

Find the zeros of 4x^2-24x+16=0

The zeros of 4x^2-24x+16=0 are x=3+sqrt(5),x=3-sqrt(5)

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4 x^{2} - 24 x + 16 = 0

x = 3 + 5, x = 3 - 5

Decimal Notation

x = 5.23606 \dots, x = 0.76393 \dots

Solution steps

4 x^{2} - 24 x + 16 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 24 ) \pm ( - 24 ) ^{2} - 4 \cdot 4 \cdot 16}{2 \cdot 4}

(- 24)^{2} - 4 \cdot 4 \cdot 16 = 85

x_{1, 2} = \frac{- ( - 24 ) \pm 8 5}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- ( - 24 ) + 8 5}{2 \cdot 4}, x_{2} = \frac{- ( - 24 ) - 8 5}{2 \cdot 4}

x = \frac{- ( - 24 ) + 8 5}{2 \cdot 4} : 3 + 5

x = \frac{- ( - 24 ) - 8 5}{2 \cdot 4} : 3 - 5

The solutions to the quadratic equation are:

x = 3 + 5, x = 3 - 5

3 x^{2} - 6 x - 36 = 0

(x - 6)^{2} = 20

(x - 6)^{2} = 12

(x - 6)^{2} = - 4

2 x^{2} - 11 x = - 15

What are the solutions to the equation 4x^2-24x+16=0 ?
The solutions to the equation 4x^2-24x+16=0 are x=3+sqrt(5),x=3-sqrt(5)
Find the zeros of 4x^2-24x+16=0
The zeros of 4x^2-24x+16=0 are x=3+sqrt(5),x=3-sqrt(5)