What are the solutions to the equation (x^2)/4+((2x+5)^2)/9 =1 ?

The solutions to the equation (x^2)/4+((2x+5)^2)/9 =1 are x=-8/5

Find the zeros of (x^2)/4+((2x+5)^2)/9 =1

The zeros of (x^2)/4+((2x+5)^2)/9 =1 are x=-8/5

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\frac{x ^{2}}{4} + \frac{( 2 x + 5 ) ^{2}}{9} = 1

x = - \frac{8}{5}

Decimal Notation

x = - 1.6

Solution steps

\frac{x ^{2}}{4} + \frac{( 2 x + 5 ) ^{2}}{9} = 1

Find Least Common Multiplier of

4, 9 : 36

Multiply by LCM=

36

\frac{x ^{2}}{4} \cdot 36 + \frac{( 2 x + 5 ) ^{2}}{9} \cdot 36 = 1 \cdot 36

Simplify

9 x^{2} + 4 (2 x + 5)^{2} = 36

Expand

9 x^{2} + 4 (2 x + 5)^{2} : 25 x^{2} + 80 x + 100

25 x^{2} + 80 x + 100 = 36

Move

36

to the left side

25 x^{2} + 80 x + 64 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 80 \pm 8 0 ^{2} - 4 \cdot 25 \cdot 64}{2 \cdot 25}

8 0^{2} - 4 \cdot 25 \cdot 64 = 0

x_{1, 2} = \frac{- 80 \pm 0}{2 \cdot 25}

x = \frac{- 80}{2 \cdot 25}

\frac{- 80}{2 \cdot 25} = - \frac{8}{5}

x = - \frac{8}{5}

The solution to the quadratic equation is:

x = - \frac{8}{5}

∣ x + 4 ∣ < 2

7 - (- 5) - 8 = - 6 - (- 9) + 9 - 2 X

15 \cdot 4

2 x^{3} + 4 x^{2} - 10 x - 12

x + 1 = 2 x + 10

What are the solutions to the equation (x^2)/4+((2x+5)^2)/9 =1 ?
The solutions to the equation (x^2)/4+((2x+5)^2)/9 =1 are x=-8/5
Find the zeros of (x^2)/4+((2x+5)^2)/9 =1
The zeros of (x^2)/4+((2x+5)^2)/9 =1 are x=-8/5