Question

Please help me :(

Solve the quadratic equation by completing the square.
x²+ 6x-4=0
First, choose the appropriate form and fill in the blanks with the correct numbers.
Then, solve the equation. Round your answer to the nearest hundredth.
If there is more than one solution, separate them with commas.
Form:
DO...
O(x+D=0
(x-1D² = 1
Х
S
?
Solution:
x = 0

Answer 1

Explanation:

x² + 6x - 4 = 0

Add 4 to both sides

x²- 6x = 4

Take the coefficient of x and divide it by 2. 6 ÷ 2 = 3

Now square the number that we got after dividing by 2. 3² = 9

Add 9 to both side of the equation.

x² - 6x + 9 = 4 + 9

x² - 6x + 9 = 13

{ This is in a² - 2ab + b² form}

x² - 2*x *3 + 3² = 13

(x - 3)² = 13

To find the solution, take square root

x -3 = √13

x - 3 = ± 3.61

x = 3.61 +3 ; x = -3.61 + 3

x = 6.61 ; x = -0.61

2)x² - 10x + 14 = 0

x² - 10x = -14

x² - 10x + 25 = -14 + 25

x² - 2*x*5 + 5² = 11

(x - 5)² = 11

Solution

x - 5 = √11

x - 5 = ±3.32

x = 3.32 +5 ; x = -3.32 + 5

x = 8.32 ; x = 1.68

x = 8.32