Use the quadratic formula to solve the quadratic equation 10x^2+5x=5x-8. Express its solutions in the form a±bi
To solve the quadratic equation 10x^2 + 5x = 5x - 8, we first need to rewrite the equation in standard form: ax^2 + bx + c = 0.
By moving all terms to one side, we get:
10x^2 + 5x - 5x + 8 = 0
10x^2 + 8 = 0
Now we can apply the quadratic formula:
The quadratic formula is given by x = (-b ± √(b^2 - 4ac)) / (2a)
For the equation 10x^2 + 8 = 0, we have:
a = 10, b = 0, c = 8
Using the quadratic formula, we can substitute these values:
x = (-0 ± √(0^2 - 4 * 10 * 8)) / (2 * 10)
Simplifying further:
x = (± √(-320)) / 20
Since we have a negative value under the square root, the solutions are complex (in the form a ± bi).
Therefore, the solutions to the quadratic equation 10x^2 + 5x = 5x - 8 are:
x = (-0 + √(-320)) / 20 = 0 + (√320)i / 20 = (√320)i/20
x = (-0 - √(-320)) / 20 = 0 - (√320)i / 20 = -(√320)i/20
Hence, the solutions are (√320)i/20 and -(√320)i/20 in the form a ± bi.
It has to be in a±bi. For example 10±7i
Apologies for the confusion. Let's solve the equation using the quadratic formula and express the solutions in the form a ± bi.
The equation is 10x^2 + 5x = 5x - 8.
Rewriting it in standard form, we have:
10x^2 + 5x - 5x + 8 = 0
10x^2 + 8 = 0
Now, applying the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 10, b = 0, and c = 8.
Substituting these values into the quadratic formula, we get:
x = (0 ± √(0^2 - 4 * 10 * 8)) / (2 * 10)
x = (± √(-320)) / 20
Since we have a negative value under the square root, the solutions are complex.
To express the solutions in the form a ± bi, we can simplify further:
x = ± √(-320) / 20
x = ± (√320)i / 20
x = (± √320)i / 20
Therefore, the solutions to the quadratic equation 10x^2 + 5x = 5x - 8 are:
x = (± √320)i / 20
In a±bi form, the solutions can be written as:
x = (± √320 / 20)i
x = (± 8√5 / 20)i
x = (± 2√5 / 5)i
Hence, the solutions are 2√5/5i and -2√5/5i in the form a ± bi.