Mathematics, 01.08.2019 11:30 arulanreddy3754

Solve the equation by completing the square. round to the nearest hundredth if necessary. x^2 +3x -5 = 0. 1.19, –4.19 –8.75, 5.75 1.66, 2.69 1.05, –4.05

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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

Answer from: kevinvalencia01

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 from: Quest

{x = -1/2 , y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer: {x = -1/2 , y = -1

Answer from: Quest

step-by-step explanation:

only stephen hawking would know.

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

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