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factorable quadratic equation and solve for the roots: 2x^2 + 13x + 20=0
In google type:
quadratic equation online
When you see list of results click on:
Free Online Quadratic Equation Solver:Solve by Quadratic Formula
When page be open click option
Solve by Factoring (includes Factoring by Grouping)
then in rectangle type
2x^2 + 13x + 20=0
and click option
solve it
the 13x in the middle indicates you will need 5 as one of the factors of 20, and it cannot be multiplied by 2, so
(2x+5)(x+4)
To solve the quadratic equation 2x^2 + 13x + 20 = 0, we need to find the roots by factoring. Here's how you can do it:
Step 1: Write down the equation in the standard form, with the quadratic term (x^2) first, followed by the linear term (x), and then the constant term.
Given equation: 2x^2 + 13x + 20 = 0
Step 2: Factorize the quadratic equation into a product of two binomials. To do this, we need to find two numbers whose product is the product of the coefficient of x^2 (2) and the constant term (20), and whose sum is equal to the coefficient of x (13).
The factors of 2 and 20 are:
- 1 × 40
- 2 × 20
- 4 × 10
- 5 × 8
Among these pairs, the pair that has a sum of 13 is 4 and 5.
Step 3: Rewrite the middle term of the quadratic equation using the two factors determined in step 2.
2x^2 + 4x + 5x + 20 = 0
Step 4: Group the terms and factor by grouping.
(2x^2 + 4x) + (5x + 20) = 0
2x(x + 2) + 5(x + 4) = 0
Step 5: Now, both terms have a common factor (x + 2). Factor it out.
(x + 2)(2x + 5) = 0
Step 6: Apply the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero.
Setting each factor equal to zero, we get two equations:
x + 2 = 0 or 2x + 5 = 0
Step 7: Solve each equation separately.
For x + 2 = 0:
x = -2
For 2x + 5 = 0:
2x = -5
x = -5/2 or x = -2.5
Therefore, the roots of the equation 2x^2 + 13x + 20 = 0 are x = -2, x = -2.5, x = -2.5.
I hope this explanation helps you understand how to solve and factor a quadratic equation. Let me know if you have any further questions!