Question

Solve the quadratic equation (x+3)²=25 by factorisation method

Answer 1

(x+3)²=25

Step 1: Simplify both sides of the equation.

x²+6x+9=25

Step 2: Subtract 25 from both sides.

x²+6x+9−25=25−25

x²+6x−16=0

Step 3: Factor left side of equation.

(x−2)(x+8)=0

Step 4: Set factors equal to 0.

x−2=0 or x+8=0

x=2 or x=−8

Answer:

x=2 or x=−8

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Answer 2

Given,

$(x + 3) ^{2} = 25$

To find,

The solution of the given quadratic equation by factorization method.

Solution,

The values of x after factorising $(x + 3) ^{2} = 25$ are -8 and 2.

We can easily solve this problem by following the given steps.

According to the question,

We have the following expression:

$(x + 3) ^{2} = 25$

Now, we can expand the left-hand side using the identity: (a+b)² = a²+b²+2ab. In this case, we have a = x and b = 3.

x²+(3)²+2(x)(3) = 25

x²+9+6x = 25

Moving 25 from the right-hand side to the left-hand side,

x²+6x+9-25 = 0

x²+6x-16 = 0

Now, we can factorise this expression by splitting the middle term such that their subtraction gives 6x and multiplication gives (-16×x²).

These two terms are 8x and -2x.

x²+8x-2x-16 = 0

Taking x common from the first two terms and -2 common from the last two terms,

x(x+8)-2(x+8) = 0

Taking (x+8) common,

(x+8)(x-2) = 0

(x+8) = 0 and (x-2) = 0

x = -8 and x = 2

Hence, the values of x after factorising the given quadratic equation are -8 and 2.