Solving Equations: Quadratic & More!

In summary, to solve the equation 3(x-3) + 4x+7= 5x-3, distribute 3(x-3) and group the x's on one side of the equation and the rest of the numbers on the other side. For the quadratic equations x^2 + 7x + 12 = 0, 3x^2 - 10x + 8 = 0, and 8y^2 + 18y = 5 = 0, try factoring or using the quadratic formula to find the solutions. The quadratic formula is given by x_{1,2} = \frac{{ - b \pm \sqrt {b^2 - 4ac
  • #1
Nicholasw
5
0
How would I solve this equation:

3(x-3) + 4x+7= 5x-3

And How would I solve these Quadratic Equation:

x^2 + 7x + 12 = 0

3x^2 - 10x + 8 = 0

8y^2 + 18y = 5 = 0

Thanks.
 
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  • #2
For the first one, distribute [tex]3(x-3)[/tex] and the group the x's on one side of the equation, and the rest of the numbers on the other side.

For the quadratics, try factoring. If you don't want to use that method, you can always use the quadratic formula.

Jameson
 
  • #3
Nicholasw said:
3(x-3) + 4x+7= 5x-3
Simplify it by working out the paranthesis and put everything in x on 1 side, this should give an easy lineair equation.

Nicholasw said:
x^2 + 7x + 12 = 0

3x^2 - 10x + 8 = 0

8y^2 + 18y = 5 = 0
Have you seen the quadratic formula to solve these solutions? If an equation is given in the form [itex]ax^2 + bx + c = 0[/itex], then the solutions are given by:

[tex]x_{1,2} = \frac{{ - b \pm \sqrt {b^2 - 4ac} }}
{{2a}}[/tex]
 

1. What is a quadratic equation?

A quadratic equation is a polynomial equation of the second degree that can be written in the form ax² + bx + c = 0, where a, b, and c are constants and x is the variable. It is also known as a second-degree equation because the highest degree of the variable is 2.

2. How can I solve a quadratic equation?

To solve a quadratic equation, you can use different methods such as factoring, completing the square, or using the quadratic formula. These methods involve manipulating the equation to isolate the variable on one side and find its value through various mathematical operations.

3. What is the discriminant in a quadratic equation?

The discriminant in a quadratic equation is the part of the quadratic formula under the square root sign: b² - 4ac. It helps determine the nature of the solutions to the equation. If the discriminant is positive, the equation has two distinct real solutions. If the discriminant is zero, the equation has one real solution. If the discriminant is negative, the equation has two complex solutions.

4. Can a quadratic equation have no solution?

Yes, a quadratic equation can have no solution. This happens when the discriminant is negative. Since the square root of a negative number is not a real number, the equation has no real solutions. However, it may have complex solutions in the form of a+bi, where a and b are real numbers and i is the imaginary unit.

5. How are quadratic equations used in real life?

Quadratic equations have many applications in real life, such as in physics, engineering, and economics. They can be used to model the trajectory of a projectile, determine the shape of a satellite's orbit, or optimize profits in business. They are also used in fields like architecture, computer graphics, and cryptography.

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