Question

9x^2-75 x+6=0 by completing square method

Answer 1

Answer:

Given:

Quadratic equation =$9 {x}^{2} - 75x + 6 = 0$

What to find = (zeroes of the quadratic equation)?

Solution :

Factorise by completing the square

$9 {x}^{2} - 75x + 6 = 0$

Divide both sides by 3

$\frac{9 {x}^{2} }{3} - \frac{75x}{3} + \frac{2}{3} = 0$

Move the number term to the right side of the equation.

$3 {x}^{2} - 25x = - 2$

Divide both sides by 3

$\frac{3 {x}^{2} }{3} - \frac{25x}{3} = \frac{ - 2}{3}$

Complete the square on the left side of the equation and balance this by adding the same number to the right side of the equation.

Complete the square on the left side of the equation and balance this by adding the same number to the right side of the equation. Add

$( \frac{25}{6} ) {}^{2}$

To both sides of the equation

${x}^{2} - \frac{25x}{3} + ( \frac{25}{6} ) {}^{2} = \frac{ - 2}{3} + ( \frac{25}{6} ) {}^{2}$

On the left side of the equation we get a formula

$(a + b) {}^{2}$

So,

$(x - \frac{25}{6} ) {}^{2} = - \frac{2}{3} + ( \frac{25}{6} ) {}^{2}$

Take the square root on both sides of the equation.

$\sqrt({x - \frac{25}{6} } ) {}^{2} = \sqrt{ \frac{601}{36} } \\ = x - \frac{25}{6} = ± \frac{ \sqrt{601} }{6} \\ = x_1 = \frac{ \sqrt{601} }{6} + \frac{25}{6} \\ = x = \frac{ \sqrt{601} + 25}{6}$

And

$x_2 = \frac{ \sqrt{601} - 25}{6}$

*Extra:✈

Quadratic equation : A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared. The standard form is ax² + bx + c = 0 with a, b, and c being constants, or numerical coefficients, and x is an unknown variable. One absolute rule is that the first constant "a" cannot be a zero.

Steps to solve a quadratic equation by completing the square method :

1. Divide all terms by a[the coefficient of x2].
2. Move the number term [c/a] to the right side of the equation.
3. Complete the square on the left side of the equation and balance this by adding the same value to the right side of the equation.
4. Take the square root on both sides of the equation.
5. Subtract the number that remains on the left side of the equation to find x.