Answer:
x = -7, x = 3
Explanations:
The given equation is:
[tex]4x^2+16x-84=0[/tex]
To solve by completeting the square method, follow the steps below.
Step 1: Divide throough by 4
[tex]\begin{gathered} \frac{4x^2}{4}+\frac{16x}{4}-\frac{84}{4}=\text{ 0} \\ x^2+4x-21\text{ = 0} \end{gathered}[/tex]
Step 2: Take the constant(-21) to the right side of the equality sign
[tex]x^2+4x=21[/tex]
Step 3: Find the half of 4, (I.e. 2), and add its square to both sides of the equation
[tex]\begin{gathered} x^2+4x+2^2=21+2^2 \\ x^2+4x+2^2=\text{ 25} \end{gathered}[/tex]
Step 4: Factorise the Left Hand side of the equation. It becomes
[tex](x+2)^2=\text{ 25}[/tex]
Step 5: Find the square root of both sides
[tex]\begin{gathered} \sqrt[]{(x+2)^2}=\text{ }\sqrt[]{25} \\ x\text{ + 2 = }\pm5\text{ } \end{gathered}[/tex]
Step 6: Collect like terms
[tex]\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}[/tex]
The solutions to the quadratic equation are x = -7, x = 3
