Is(2x-7)^2=(x+1)^2 a quadratic equation ?

Question

and How to write it in standard form?

Answer 1

• The general form of a quadratic equation is ax² + bx + c = 0.

The equation is (2x - 7)² = (x + 1)² .

4x² - 28x + 49 = x² + 2x + 1

4x² - 28x + 49 - x² - 2x - 1 = 0

3x² - 30x + 48 = 0.

3x² - 30x + 48 = 0, is a quadratic equation.

• Standard form of a quadratic equation :
• A quadratic equation ax² + bx + c = 0 can be expressed in the standard form a(x - h)² + k = 0 ,By completing the square.
• Once in standard form, the vertex is given by (h, k).
• The parabola opens up if a > 0 and opens down if a < 0.

The quadratic equation is 3x² - 30x + 48 = 0.

Step 1 :

The coefficient of x² is 3, so, factor 3 out of each x term.

3(x² - 10x + 16) = 0

x² - 10x + 16 = 0

Step 2 :

To change the expression into a perfect square trinomial add (half the x coefficient)² to each side of the expression

 Here x coefficient = - 10. so, (half the x coefficient)² = (- 10/2)²= 25.

Add 25 to each side.

x² - 10x + 25 + 16 = 0 + 25

Step 3:

(x - 5)² + 16 = 25

Step 4:

(x - 5)² + 16 - 25 = 0

Step 5:

(x - 5)² - 9 = 0.

This is the standard form of the quadratic equation 3x² - 30x + 48 = 0.