Solve the following equation using the quadratic formula.
2x2−1=9x
To use the quadratic formula, we first need to write the equation in standard form:
2x^2 - 9x - 1 = 0
Now we can apply the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions for x can be found using:
x = (-b ± √(b^2 - 4ac))/(2a)
In this case, a = 2, b = -9, and c = -1. Substituting these values into the quadratic formula:
x = (-(-9) ± √((-9)^2 - 4(2)(-1)))/(2(2))
x = (9 ± √(81 + 8)) / 4
x = (9 ± √(89)) / 4
Therefore, the solutions to the equation are:
x = (9 + √89)/4
and
x = (9 - √89)/4
To solve the equation 2x^2 - 1 = 9x using the quadratic formula, we first need to rearrange the equation in standard quadratic form, which is ax^2 + bx + c = 0.
So, let's bring all terms to one side:
2x^2 - 9x - 1 = 0
Now, we can identify the coefficients:
a = 2
b = -9
c = -1
Next, we can substitute these values into the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values:
x = (-(-9) ± √((-9)^2 - 4(2)(-1))) / (2(2))
Simplifying further:
x = (9 ± √(81 + 8)) / 4
x = (9 ± √89) / 4
Therefore, the solutions to the equation 2x^2 - 1 = 9x using the quadratic formula are:
x = (9 + √89) / 4
x = (9 - √89) / 4
To solve the equation, we need to use the quadratic formula, which is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c = 0.
For the given equation: 2x^2 - 1 = 9x, we need to rearrange it to put it in standard form, which is ax^2 + bx + c = 0.
So, let's move all terms to one side to get: 2x^2 - 9x - 1 = 0.
Now, we can identify the coefficients:
- a = 2
- b = -9
- c = -1
By substituting these values into the quadratic formula, we can solve for x:
x = [ -(-9) ± √((-9)^2 - 4(2)(-1)) ] / (2(2))
Simplifying further:
x = [ 9 ± √(81 + 8) ] / 4
x = [ 9 ± √(89) ] / 4
Hence, the solutions to the equation 2x^2 - 1 = 9x are:
x = (9 + √89) / 4
x = (9 - √89) / 4