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Use the quadratic formula to solve the equation.
x^2+5x−7=0
To solve the equation x^2 + 5x - 7 = 0 using the quadratic formula, we first identify the values of a, b, and c in the general quadratic equation ax^2 + bx + c = 0.
In this case, a = 1, b = 5, and c = -7.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the given values, we have:
x = (-(5) ± √((5)^2 - 4(1)(-7))) / (2(1))
x = (-5 ± √(25 + 28)) / 2
x = (-5 ± √(53)) / 2
Therefore, the solutions to the quadratic equation x^2 + 5x - 7 = 0 are:
x1 = (-5 + √(53)) / 2
x2 = (-5 - √(53)) / 2
To use the quadratic formula to solve the equation x^2 + 5x - 7 = 0, we need to first identify the values of the coefficients a, b, and c in the general quadratic equation form: ax^2 + bx + c = 0.
In this case, a = 1, b = 5, and c = -7.
Now we can substitute these values into the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a).
Plugging in the values, we get:
x = (-5 ± √(5^2 - 4(1)(-7))) / (2(1)).
Simplifying further, we have:
x = (-5 ± √(25 + 28)) / 2.
x = (-5 ± √53) / 2.
Therefore, the solutions to the equation x^2 + 5x - 7 = 0 are:
x = (-5 + √53) / 2.
x = (-5 - √53) / 2.
To solve the equation x^2 + 5x - 7 = 0 using the quadratic formula, we will follow these steps:
Step 1: Identify the coefficients a, b, and c in the quadratic equation that is in the form ax^2 + bx + c = 0.
In our equation, a = 1, b = 5, and c = -7.
Step 2: Substitute the values of a, b, and c into the quadratic formula.
The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a).
Step 3: Plug in the values of a, b, and c into the quadratic formula.
x = (-(5) ± √((5)^2 - 4(1)(-7))) / (2(1)).
Step 4: Simplify the equation inside the square root.
x = (-5 ± √(25 + 28)) / 2.
Step 5: Further simplify the square root.
x = (-5 ± √53) / 2.
Step 6: Split the equation into two separate equations.
x = (-5 + √53) / 2, and x = (-5 - √53) / 2.
These are the two solutions to the quadratic equation x^2 + 5x - 7 = 0 using the quadratic formula.