x^2+6x=24
x^2 +6x+9=24+9
(X+3)^2=33
x+3=sqrt(33)
x=+-sqrt(33)-3
or look up Quadratic formula
looks like it does not factor, so...
in this case I would complete the square.
x^2 + 6x + 9 = 24 + 9
(x+3)^2 = 33
x+3 = ± √ 33
x = -3 ± √33
If a quadratic does not factor and the first term is
1x^2 with an even number as the x coefficient, completing the square is faster than using the formula. Secondly, completing the square gives you the simplified answer, whereas with the formula you still have to simplify the final answer.
Try it by using the formula for the above to get the same answer
To solve the equation x^2 + 6x = 24, you can follow these steps:
Step 1: Make sure the equation is in standard form, which is ax^2 + bx + c = 0. In this case, the equation is already in standard form.
Step 2: To solve a quadratic equation like this, you can use various methods such as factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula in this case.
The quadratic formula is given by:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
In our equation x^2 + 6x = 24, we have:
a = 1 (coefficient of x^2)
b = 6 (coefficient of x)
c = -24 (constant term)
Step 3: Substitute the values of a, b, and c into the quadratic formula:
x = (-6 ± sqrt(6^2 - 4*1*(-24))) / (2*1)
Step 4: Simplify the expression inside the square root:
x = (-6 ± sqrt(36 + 96)) / 2
x = (-6 ± sqrt(132)) / 2
Step 5: Calculate the value of the square root:
x = (-6 ± sqrt(4 * 33)) / 2
x = (-6 ± 2sqrt(33)) / 2
Step 6: Simplify the expression:
x = -3 ± sqrt(33)
So, the solutions to the equation x^2 + 6x = 24 are:
x = -3 + sqrt(33) and x = -3 - sqrt(33)