Sure! Let's solve the equation step-by-step:
The given equation is:
[tex]\[ 4(x + 7)^2 = 25 \][/tex]
1. Divide both sides by 4 to isolate the squared expression:
[tex]\[ (x + 7)^2 = \frac{25}{4} \][/tex]
[tex]\[ (x + 7)^2 = 6.25 \][/tex]
2. Take the square root of both sides to remove the square:
[tex]\[ x + 7 = \pm \sqrt{6.25} \][/tex]
Since [tex]\(\sqrt{6.25} = 2.5\)[/tex], we have:
[tex]\[ x + 7 = \pm 2.5 \][/tex]
3. Solve for [tex]\(x\)[/tex] by considering the two possible cases:
- For the positive root:
[tex]\[ x + 7 = 2.5 \][/tex]
[tex]\[ x = 2.5 - 7 \][/tex]
[tex]\[ x = -4.5 \][/tex]
- For the negative root:
[tex]\[ x + 7 = -2.5 \][/tex]
[tex]\[ x = -2.5 - 7 \][/tex]
[tex]\[ x = -9.5 \][/tex]
So, the solutions to the equation [tex]\( 4(x + 7)^2 = 25 \)[/tex] are:
[tex]\[ x = -4.5 \][/tex]
[tex]\[ x = -9.5 \][/tex]
