Solve the equation for real solutions by the quadratic formula.
9x2−5x−7=0
To solve the equation 9x^2 - 5x - 7 = 0 using the quadratic formula, we first identify the coefficients of the variables:
a = 9
b = -5
c = -7
Then, we substitute these values into the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
Plugging in the values, we get:
x = (-(-5) ± sqrt((-5)^2 - 4(9)(-7))) / (2(9))
Simplifying further:
x = (5 ± sqrt(25 + 252)) / 18
x = (5 ± sqrt(277)) / 18
Therefore, the real solutions to the equation 9x^2 - 5x - 7 = 0 are:
x = (5 + sqrt(277)) / 18
x = (5 - sqrt(277)) / 18
The given equation is 9x^2 - 5x - 7 = 0. We can use the quadratic formula to solve for the value of x.
The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In our given equation, a = 9, b = -5, and c = -7. Let's substitute these values into the formula and simplify:
x = (-(-5) ± √((-5)^2 - 4 * 9 * (-7))) / (2 * 9)
x = (5 ± √(25 + 252)) / 18
x = (5 ± √(277)) / 18
Therefore, the solutions for the given equation are:
x = (5 + √277) / 18
x = (5 - √277) / 18
These are the real solutions for the equation 9x^2 - 5x - 7 = 0 using the quadratic formula.
To solve the equation 9x^2 - 5x - 7 = 0 using the quadratic formula, we need to identify the values of coefficients a, b, and c in the equation ax^2 + bx + c = 0. In this case, a = 9, b = -5, and c = -7.
The quadratic formula states that for any 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)
Now let's substitute the values of a, b, and c into the quadratic formula:
x = (-(-5) ± √((-5)^2 - 4(9)(-7))) / (2(9))
Simplifying further:
x = (5 ± √(25 + 252)) / 18
x = (5 ± √(625)) / 18
Taking the square root:
x = (5 ± 25) / 18
Now we have two possibilities:
x₁ = (5 + 25) / 18 = 30 / 18 = 5/3
x₂ = (5 - 25) / 18 = -20 / 18 = -10/9
Hence, the real solutions for the equation 9x^2 - 5x - 7 = 0 are x = 5/3 and x = -10/9.