Question

Solve the equation by completing the square. Round to the nearest hundredth if necessary. x^2 +3x -5 = 0.

Answer 1

Answer:

1.19, –4.19 are correct option .

Step-by-step explanation:

Given : x² +3x -5 = 0.

To find : Solve the equation by completing the square. Round to the nearest hundredth .

Solution : We have given that

x² +3x -5 = 0.

On multiplying and divide by 2 to the term 3x .

x² + $\frac{2}{2}$ * 3x -5 = 0.

On adding and subtracting the square of $\frac{3}{2}$

$x^{2} + 2 * \frac{3x}{2} +(\frac{3}{2}) ^{2} - (\frac{3}{2} )^{2} - 5 = 0$.

We can see first three terms are square

$(x+ \frac{3}{2} )^{2}$ - $(\frac{3}{2}) ^{2}$ -5 = 0

$(x+ \frac{3}{2} )^{2}$ - $(\frac{9}{4})$ -5 =0

On solving

$(x+ \frac{3}{2} )^{2}$ - $(\frac{29}{4})$  =0

On adding both sides by  $(\frac{29}{4})$

$(x+\frac{3}{2} )^{2}$ = $(\frac{29}{4})$

Taking square root

$(x+\frac{3}{2})$ = ± $\sqrt{\frac{29}{4} }$.

$(x+\frac{3}{2})$  = ± ${\frac{5.38}{2} }$.

$(x+\frac{3}{2})$  = ± 2.69 (it has two sign , so we will solve for both)

For + 2.69

On subtracting $(\frac{3}{2})$ both side.

$(x+\frac{3}{2})$  = + 2.69

x = + 2.69 - $(\frac{3}{2})$

x = $(\frac{5.38 -3}{2})$.

x =  $(\frac{2.38}{2})$.

x = 1.19

For - 2.69

On subtracting $(\frac{3}{2})$ both side.

$(x+\frac{3}{2})$  = - 2.69

x = - 2.69 - $(\frac{3}{2})$

x =  $(\frac{-5.38 -3}{2})$.

x =  $(\frac{-8.38}{2})$.

x = - 4.19.

Therefore, 1.19, –4.19 are correct option .

Answer 2

X^2 + 3x - 5 = 0
x^2 + 3x = 5
x^2 + 3x + 2.25 = 5 + 2.25
(x + 1.5)^2 = 7.25
x + 1.5 = (+-) sqrt 7.25
x = -1.5 (+-) 2.69

x = -1.5 + 2.69 = 1.19 <=== ur answer
x = -1.5 - 2.69 = -4.19 <=== ur answer