Use the Quadratic Formula to solve the equation. (Enter your answers as a comma-separated list.) 13x^2 + 1= -10x
Hmm lets see... I cant write the answers in because it will just say letters 😢 but if you want the answers go to symbolab you can type that in their :D have a nice day and stay safe
First, put it into standard form
13x^2 + 1= -10x
13x^2 + 10x + 1 = 0
then apply the formula, and you get
x = (-10±√(10^2-4*13*1))/(2*13)
yeah kind of like that
13x² + 10 x + 1 = 0
a = 13 , b = 10 , c = 1
x½ = [ - b ± √ ( b² - 4 a c ) ] / 2 a
x½ = [ - 10 ± √ ( 10² - 4 ∙ 13 ∙ 1 ) ] / 2 ∙ 13 = [ - 10 ± √ ( 100 - 52 ) ] / 26 =
( - 10 ± √48 ) / 26 = [ - 10 ± √ (16 ∙ 3 ) ] / 26 = ( - 10 ± √16 ∙ √3 ) / 26 =
( - 10 ± 4√3 ) / 26 = ( - 2 ∙ 5 ± 2 ∙ 2 √3 ) / 26 = 2 ( - 5 ± 2 √3 ) / 2 ∙ 13
x½ = ( - 5 ± 2√3 ) / 13
x1 = ( - 5 - 2√3 ) / 13 = - 5 / 13 - 2√3 / 13
x 2 = ( - 5 + 2√3 ) / 13 = - 5 / 13 + 2√3 / 13
The solutions are:
- 5 / 13 - 2√3 / 13 , - 5 / 13 + 2√3 / 13
To solve the quadratic equation 13x^2 + 1 = -10x using the Quadratic Formula, we need to rearrange the equation in the standard form: ax^2 + bx + c = 0.
In this case, we have:
13x^2 + 10x + 1 = 0
Now, we can identify the coefficients:
a = 13
b = 10
c = 1
Next, we can apply the Quadratic Formula, which states that for an equation in the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the values from our equation:
x = (-(10) ± √((10)^2 - 4(13)(1))) / (2(13))
Simplifying further:
x = (-10 ± √(100 - 52)) / 26
x = (-10 ± √(48)) / 26
x = (-10 ± √(16 * 3)) / 26
x = (-10 ± 4√3) / 26
The solution to the equation is x = (-10 + 4√3) / 26, (-10 - 4√3) / 26.