What are the solutions to the equation (x+a)(x-a)+4a(a-x)=0 ?

The solutions to the equation (x+a)(x-a)+4a(a-x)=0 are x=3a,x=a

Find the zeros of (x+a)(x-a)+4a(a-x)=0

The zeros of (x+a)(x-a)+4a(a-x)=0 are x=3a,x=a

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(x + a) (x - a) + 4 a (a - x) = 0

x = 3 a, x = a

Solution steps

(x + a) (x - a) + 4 a (a - x) = 0

Expand

(x + a) (x - a) + 4 a (a - x) : x^{2} + 3 a^{2} - 4 a x

x^{2} + 3 a^{2} - 4 a x = 0

Write in the standard form

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

x^{2} - 4 a x + 3 a^{2} = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 4 a ) \pm ( - 4 a ) ^{2} - 4 \cdot 1 \cdot 3 a ^{2}}{2 \cdot 1}

Simplify

(- 4 a)^{2} - 4 \cdot 1 \cdot 3 a^{2} : 2 a

x_{1, 2} = \frac{- ( - 4 a ) \pm 2 a}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 4 a ) + 2 a}{2 \cdot 1}, x_{2} = \frac{- ( - 4 a ) - 2 a}{2 \cdot 1}

x = \frac{- ( - 4 a ) + 2 a}{2 \cdot 1} : 3 a

x = \frac{- ( - 4 a ) - 2 a}{2 \cdot 1} : a

The solutions to the quadratic equation are:

x = 3 a, x = a

x, (x + 5)^{2} = 2 y

100 = 2 \frac{0.25}{3} \cdot 21.91 \cdot (π \cdot a \cdot 0.008)^{2}

8 x^{2} - 10 x - 3 = 0

x^{2} - 3 x = - 20

1 0^{2} = 8^{2} + b^{2}

What are the solutions to the equation (x+a)(x-a)+4a(a-x)=0 ?
The solutions to the equation (x+a)(x-a)+4a(a-x)=0 are x=3a,x=a
Find the zeros of (x+a)(x-a)+4a(a-x)=0
The zeros of (x+a)(x-a)+4a(a-x)=0 are x=3a,x=a