What are the solutions to the equation (3+2x)^2=(4-x)^2 ?

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

Find the zeros of (3+2x)^2=(4-x)^2

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

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(3 + 2 x)^{2} = (4 - x)^{2}

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

Decimal Notation

x = 0.33333 \dots, x = - 7

Solution steps

(3 + 2 x)^{2} = (4 - x)^{2}

Expand

(3 + 2 x)^{2} : 9 + 12 x + 4 x^{2}

Expand

(4 - x)^{2} : 16 - 8 x + x^{2}

9 + 12 x + 4 x^{2} = 16 - 8 x + x^{2}

Move

x^{2}

to the left side

9 + 12 x + 3 x^{2} = 16 - 8 x

Move

8 x

to the left side

3 x^{2} + 20 x + 9 = 16

Move

16

to the left side

3 x^{2} + 20 x - 7 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 20 \pm 2 0 ^{2} - 4 \cdot 3 ( - 7 )}{2 \cdot 3}

2 0^{2} - 4 \cdot 3 (- 7) = 22

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

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

c = 3100 - c^{2}

- 4.9 x^{2} + 10 x + 20 = 0

5 x^{2} + 3 x - 4

x^{2} + 10

17 = b^{2}

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