Solving quadriatic equaitons using factoring.
X^2-6=30-3x^2
The answer in the book is -3,3.
I have tried to work the problem several times. I am not getting this answer.
X^2-6=30-3x^2
4x^2 = 36
x^2 = 9
x = ±3
To solve the quadratic equation using factoring, we need to first rearrange the equation and set it equal to zero. Let's simplify the given equation:
x^2 - 6 = 30 - 3x^2
Rearranging the terms:
x^2 + 3x^2 = 30 + 6
Combining like terms:
4x^2 = 36
Now, let's bring everything to one side to have a standard quadratic equation:
4x^2 - 36 = 0
To factor this quadratic equation, we look for two numbers whose product is equal to the product of the coefficient of x^2 (4) and the constant term (-36), and whose sum is equal to the coefficient of x (0). In this case, the numbers are -3 and 3.
So, we can rewrite the equation factored as:
(2x - 6)(2x + 6) = 0
Setting each factor equal to zero:
2x - 6 = 0 and 2x + 6 = 0
Solving each equation:
For 2x - 6 = 0:
2x = 6
x = 6/2
x = 3
For 2x + 6 = 0:
2x = -6
x = -6/2
x = -3
Therefore, the solutions to the quadratic equation x^2 - 6 = 30 - 3x^2 are x = -3 and x = 3.