use the quadratic formula to solve the equation
x^2+5x-7=0
sho all steps
To solve the equation using the quadratic formula, first identify the coefficients of the equation:
a = 1
b = 5
c = -7
Next, substitute these values into the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Now, plug in the values:
x = (-(5) ± √((5)^2 - 4(1)(-7))) / (2(1))
Simplify:
x = (-5 ± √(25 + 28)) / 2
x = (-5 ± √(53)) / 2
Therefore, the two solutions to the equation x^2 + 5x - 7 = 0 are:
x = (-5 + √(53)) / 2
x = (-5 - √(53)) / 2
To solve the quadratic equation x^2 + 5x - 7 = 0 using the quadratic formula, we need to substitute the coefficients of the equation into the formula and then simplify.
The quadratic formula is:
x = (-b ± √(b^2 - 4ac)) / 2a
In our equation, a = 1, b = 5, and c = -7. Now let's substitute these values into the formula:
x = (-5 ± √(5^2 - 4 * 1 * -7)) / (2 * 1)
Step 1: Simplify within the square root:
x = (-5 ± √(25 + 28)) / 2
Step 2: Continue simplifying within the square root:
x = (-5 ± √53) / 2
Step 3: Now we have two possible solutions:
x = (-5 + √53) / 2
and
x = (-5 - √53) / 2
These are the two solutions to the quadratic equation x^2 + 5x - 7 = 0.
To solve the equation x^2 + 5x - 7 = 0 using the quadratic formula, which is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
where a, b, and c are the coefficients of the quadratic equation, follow these steps:
Step 1: Identify the coefficients of the quadratic equation
In the equation x^2 + 5x - 7 = 0, the coefficients are:
a = 1
b = 5
c = -7
Step 2: Substitute the values into the quadratic formula
Now, substituting the values into the quadratic formula, we have:
x = (-(5) ± √((5)^2 - 4(1)(-7))) / (2(1))
x = (-5 ± √(25 + 28)) / 2
x = (-5 ± √53) / 2
Step 3: Simplify the equation
The equation after simplification is:
x = (-5 + √53) / 2 or x = (-5 - √53) / 2
So, the solutions to the equation x^2 + 5x - 7 = 0 using the quadratic formula are:
x = (-5 + √53) / 2 or x = (-5 - √53) / 2