What are the solutions to the equation 4x^2-12x-(x+5)^2=-32 ?

The solutions to the equation 4x^2-12x-(x+5)^2=-32 are x=7,x= 1/3

Find the zeros of 4x^2-12x-(x+5)^2=-32

The zeros of 4x^2-12x-(x+5)^2=-32 are x=7,x= 1/3

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4 x^{2} - 12 x - (x + 5)^{2} = - 32

x = 7, x = \frac{1}{3}

Decimal

x = 7, x = 0.33333 \dots

Solution steps

4 x^{2} - 12 x - (x + 5)^{2} = - 32

Expand

4 x^{2} - 12 x - (x + 5)^{2} : 3 x^{2} - 22 x - 25

3 x^{2} - 22 x - 25 = - 32

Move

32

to the left side

3 x^{2} - 22 x + 7 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 22 ) \pm ( - 22 ) ^{2} - 4 \cdot 3 \cdot 7}{2 \cdot 3}

(- 22)^{2} - 4 \cdot 3 \cdot 7 = 20

x_{1, 2} = \frac{- ( - 22 ) \pm 20}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 22 ) + 20}{2 \cdot 3}, x_{2} = \frac{- ( - 22 ) - 20}{2 \cdot 3}

x = \frac{- ( - 22 ) + 20}{2 \cdot 3} : 7

x = \frac{- ( - 22 ) - 20}{2 \cdot 3} : \frac{1}{3}

The solutions to the quadratic equation are:

x = 7, x = \frac{1}{3}

25 - 2 x^{2} = 0

(x + 1)^{2} - 3 = 0

x^{2} - 200 x + 9600 = 0

x^{2} + 10 x + c

a^{2} - 6 a - 40 = 0

What are the solutions to the equation 4x^2-12x-(x+5)^2=-32 ?
The solutions to the equation 4x^2-12x-(x+5)^2=-32 are x=7,x= 1/3
Find the zeros of 4x^2-12x-(x+5)^2=-32
The zeros of 4x^2-12x-(x+5)^2=-32 are x=7,x= 1/3