How to use the quadratic formula

Question

Solve the equation 3x² - 6x = 1.

Answer 1

Can you calculate the two solutions and answer?

Answer 2

3x ² - 6X = 1. Solve using the quadratic equation.

First set left side of equation = 0, by subtracting 1 from both sides of the equation:

3X ² - 6X -1 =0

Use quadratic equation to solve for the two values of X.

A generic quadratic equation is of the form ax ² + bx + c = 0.

The quadratic formula for solving the quadratic equation for the two values of X is:

{-b ± √ (b ²- 4ac)} / 2a

Substituting the actual values for the variables in the quadratic formula above we get:

{ 6 ± √ (6 ² - 4*3*-1)} / 2*3 =

{6 ± √ (36 - -12)} / 6 =

{6 ± √ (48) / 6

6/6 ± (4 √ 3)/6 =

1 ± 2 √ 3 / 3

X = 1 + 2/3 √ 3

X = 1 - 2/3 √ 3

Answer 3

Answer 4

Hi Asked

First make sure you understand the Quadratic Formula and its purpose. The Quadratic Formula can be used to solve any Quadratic Equation; ax² + bx + c = 0

Secondly write down the Quadratic Formula to see the variables you will be dealing with

Quadratic Formula

x = (-b±((b² - 4ac))^1/2)/2a

So you need a, b, and c as they appear in the Quadratic Equation

Finally write down your equation as given to see if it is in the correct format or needs some manipulation to be in the same format as the Quadratic Equation as ax² + bx + c = 0

Your given equation

3x² - 6x = 1

Subtract 1 from both sides to get this into the form of the Quadratic Equation

3x² - 6x -1 = 0

Label a, b, and c

a = 3

b = -6

c = -1

Now just plug them into the Quadratic Formula3

x = [-(-6)±((-6)² - 4(3)(-1))^1/2] /2(3)

x = [6±((36 + 12))^1/2]/6

x = [6±(48)^1/2]/6

x = [6±4√3]/6

x = 1± ((2√3)/3)

x = 1 + ((2√3)/3) = 1 + 1.1547 = 2.155

x = 1 - ((2√3)/3) = 1 - 1.1547 = -0.155

Of course you can graph your equation at desmos.com to confirm the zeros obtained above and your y intercept of -1.

I hope this helps.

Answer 5