Could someone please check these-I had tried one last night but it was really wrong so I'm been working-hopefully these are correct.
What are the roots of the equation and answers have to be simplified
2x^2 + 5x-10 =0
2x^2 + 5x-10+10=0+10
2x^2 + 5x = 10
2x^2 + 5x/2 = 10/2
2x^2/2 + 5x/2 = 5
x^2 + 5/2x = 5
(5/2 * 1/2)^2 = 5/4^2
x^2 + 5/2x + (5/4)^2 = 5 + (5/4)^2
(x+5/4)^2 = 105/16
x + 5/4 = +minus sqrt 105/16 = sqrt 3^1 * 5^1*7^1 = sqrt 105/4
x= -5/4 + sqrt105/4 or x= -5/4 - sqrt 105/4 Is this correct and simplified thank you Someone suggested a site that will do it but I want to learn on my own
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 in rectangle type:
2x^2 + 5x = 10
and click option:
solve it!
You wil see solution step-by-step.
To solve the equation 2x^2 + 5x - 10 = 0, you can use the quadratic formula or factoring method. Let's go through the factoring method since it seems like you were trying to simplify the equation.
1. Start with the equation: 2x^2 + 5x - 10 = 0.
2. Try to factorize the equation. In this case, since the coefficient of x^2 is 2, you can factor out a 2 from the entire equation: 2(x^2 + (5/2)x - 5) = 0.
3. Now, you need to factorize the quadratic term (x^2 + (5/2)x - 5). To find two numbers that multiply to -5 and add up to (5/2), you can use trial and error or the quadratic formula.
4. By using trial and error or the quadratic formula, you can find that the factors of the quadratic term are (x + 5) and (x - 1). Therefore, the factored form of the equation becomes: 2(x + 5)(x - 1) = 0.
5. Apply the zero product property, which states that if a product of factors equals zero, then at least one of the factors must equal zero. In this case, 2(x + 5)(x - 1) = 0 implies that either 2 = 0 or (x + 5) = 0 or (x - 1) = 0.
6. Solve each factor separately:
- For 2 = 0, since 2 is not equal to zero, this case is not valid.
- For (x + 5) = 0, you can subtract 5 from both sides of the equation to get x = -5.
- For (x - 1) = 0, you can add 1 to both sides of the equation to get x = 1.
7. The solutions to the equation are x = -5 and x = 1.
Therefore, the roots of the equation 2x^2 + 5x - 10 = 0 are x = -5 and x = 1.
You have correctly obtained the two roots, but let's confirm if the simplification is done correctly:
- Simplified form: x = -5/4 + sqrt(105)/4 or x = -5/4 - sqrt(105)/4.
So, yes, your simplification is correct. Good job on solving the equation and simplifying the roots!