Question

Solve 4x^2 + 16x - 84 = 0 by completing the square.

Answer 1

Answer:

x = -7, x = 3

Explanations:

The given equation is:

`4x^2+16x-84=0`

To solve by completeting the square method, follow the steps below.

Step 1: Divide throough by 4

`\begin{gathered} (4x^2)/(4)+(16x)/(4)-(84)/(4)=\text{ 0} \\ x^2+4x-21\text{ = 0} \end{gathered}`

Step 2: Take the constant(-21) to the right side of the equality sign

`x^2+4x=21`

Step 3: Find the half of 4, (I.e. 2), and add its square to both sides of the equation

`\begin{gathered} x^2+4x+2^2=21+2^2 \\ x^2+4x+2^2=\text{ 25} \end{gathered}`

Step 4: Factorise the Left Hand side of the equation. It becomes

`(x+2)^2=\text{ 25}`

Step 5: Find the square root of both sides

`\begin{gathered} \sqrt[]{(x+2)^2}=\text{ }\sqrt[]{25} \\ x\text{ + 2 = }\pm5\text{ } \end{gathered}`

Step 6: Collect like terms

`\begin{gathered} x\text{ = -2}\pm5 \\ x_1=\text{ -2+5} \\ x_1=\text{ 3} \\ x_2=\text{ -2-5} \\ x_2=\text{ -7} \end{gathered}`

The solutions to the quadratic equation are x = -7, x = 3