Cinco múltiplos del 12

7. Use the quadratic formula to find the solution(s). x² + 2x - 8 = 0

morpeh [17]

Hey there!

Use the quadratic formula to find the solution(s). x² + 2x - 8 = 0

Answer :

x = -4 or x = 2 ✅

Explanation :

Quadratic formula : ax² + bx + c = 0 where a ≠ 0

The number of real-number solutions (roots) is determined by the discriminant (b² - 4ac) :

If b² - 4ac > 0 , There are 2 real-number solutions

If b² - 4ac = 0 , There is 1 real-number solution.

If b² - 4ac < 0 , There is no real-number solution.

The roots of the equation are determined by the following calculation:

$x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}$

Here, we have :

a = 1
b = 2
c = -8

1) Calculate the discriminant :

b² - 4ac ⇔ 2² - 4(1)(-8) ⇔ 4 - (-32) ⇔ 36

b² - 4ac = 36 > 0 ; The equation admits two real-number solutions

2) Calculate the roots of the equation:

▪️ (1)

$x_1 = \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ x_1 = \frac{ - 2 - \sqrt{36} }{2(1) } \\ \\ x_1 = \frac{ - 2 - 6}{2} \\ \\ x_1 = \frac{ - 8}{2} \\ \\ \blue{\boxed{\red{x_1 = -4}}}$

▪️ (2)

$x_2 = \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ x_2 = \frac{ - 2 + \sqrt{36} }{2(1)} \\ \\ x_2 = \frac{ - 2 + 6}{2} \\ \\ x_2 = \frac{4}{2} \\ \\ \red{\boxed{\blue{x_2 = 2}}}$

>> Therefore, your answers are x = -4 or x = 2.

Learn more about quadratic equations:

brainly.com/question/27638369

6 0

2 years ago

Read 2 more answers

Seven tickets for a Broadway show cost $385. How much will only 4 tickets cost?

irina1246 [14]

Answer:

That seems a little hard-

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

Order the numbers 1.1, 0.138, 1.412 and √2 from least to greatest.

igor_vitrenko [27]

0.138, 1.1, 1.4112, and

7 0

3 years ago

Solve the following system: y = x 3 4x y = 18 (6, 3) (3, 6) (â’3, 6) (3, â’6).

Nastasia [14]

The solution of the given equation is (3,6). The correct option is B.(3,6)

<h3>Given equations,</h3>

$y=x+3.......(1)\\4x+y=18.....(2)$

<h3>How to solve the equations?</h3>

putting the value of y from equation (1) in equation (2) , we get

$4x+x+3=18\\$ $5x=18-3\\5x=15\\x=3$

substitute the value of x=3 in equation (1) we get,

$y=3+3\\y=6$

Hence, the solution of given equation is (3,6).

So, the correct option is B.

For more details about the system of equations, follow the link:

brainly.com/question/12895249

4 0

2 years ago

EXPLAIN WHY THE SYSTEM HAS THE ANSWER GIVEN. SOLVE EACH SYSTEM BY ELIMINATION TO PROVE YOUR ANSWER.

Aleonysh [2.5K]

Answer:

Step-by-step explanation:

The given system of equations is expressed as

3x + y = 9 - - - - - - - - - - - - - - -1

3x = 9 - y - - - - - - - - - - - - - -2

To apply the method of elimination, we would rearrange equation 2 so that it would take the form of equation 1. Therefore, we would add y to the left hand side and the right hand side of the equation, it becomes

3x + y = 9 - - - - - - - - - - - - - - - - -3

Subtracting equation 3 from equation 1, it becomes

0 = 0

The equations have infinitely many solutions because if we input any values of x and y that satisfies the first equation, those values will also satisfy the second equation.

6 0

3 years ago