solve by factoring
2a² - 3a = -5
In google type:
quadratic equation online
When you see list of result click on:
Free Online Quadratic Equation Solver:Solve by Quadratic Formula
When page be open in rectangle type:
2a^2-3a=-5
(Exactly in this form)
Then click option:
2a^2-3a=-5
and cilck option:
solve it!
You will see solution step-by-step.
When page be open click:
2a^2-3a=-5
Then option:
Solve by Factoring(includes Factoring by Grouping)
and cilck option:
solve it!
2a² - 3a = -5
2a² - 3a + 5 = 0
(a + 1)(2a - 5 ) = 0
a = -1 or a = 5/2
To solve the equation 2a² - 3a = -5 by factoring, we can rearrange the equation to have a zero on one side:
2a² - 3a + 5 = 0
Now, we need to factor the quadratic expression on the left-hand side. Unfortunately, this quadratic cannot be easily factored since the discriminant (b² - 4ac) is negative. As a result, we will need to use the quadratic formula to find the solutions.
The quadratic formula states that for an equation of the form ax² + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b² - 4ac)) / (2a)
In our case, a = 2, b = -3, and c = 5. Substituting these values into the quadratic formula:
a = 2
b = -3
c = 5
x = (-(-3) ± √((-3)² - 4(2)(5))) / (2(2))
= (3 ± √(9 - 40)) / 4
= (3 ± √(-31)) / 4
Since the square root of -31 is an imaginary number, we cannot simplify it further. Therefore, the solutions to the equation 2a² - 3a = -5 are:
x = (3 + √(-31)) / 4
x = (3 - √(-31)) / 4
These solutions cannot be expressed in real numbers because of the presence of the imaginary component arising from the square root of a negative number.