use the quadratic formula to solve the equation
x^2+5x-7=0
The quadratic formula is given as:
x = (-b ± √(b^2 - 4ac)) / (2a)
Comparing the equation x^2 + 5x - 7 = 0 with the standard quadratic equation ax^2 + bx + c = 0, we have:
a = 1, b = 5, and c = -7.
Substituting these values into the quadratic formula, we get:
x = (-5 ± √(5^2 - 4(1)(-7))) / (2(1))
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, follow these steps:
Step 1: Identify the values of a, b, and c.
In this equation, a = 1, b = 5, and c = -7.
Step 2: Substitute the values into the quadratic formula.
The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a).
Substituting the values, we get:
x = (-5 ± √(5^2 - 4(1)(-7))) / (2 * 1).
Step 3: Simplify the expression inside the square root.
x = (-5 ± √(25 + 28)) / 2.
x = (-5 ± √53) / 2.
Step 4: Divide the numerator by the denominator.
x = (-5 + √53) / 2 and x = (-5 - √53) / 2.
Therefore, the solutions for the equation x^2 + 5x - 7 = 0 using the quadratic formula are x = (-5 + √53) / 2 and x = (-5 - √53) / 2.
To use the quadratic formula to solve the equation x^2 + 5x - 7 = 0, follow these steps:
Step 1: Identify the coefficients of the quadratic equation. In this case, the coefficient of x^2 is 1, the coefficient of x is 5, and the constant term is -7.
Step 2: Write down the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Step 3: Substitute the coefficients into the quadratic formula. In this case:
a = 1, b = 5, and c = -7.
Step 4: Plug in the values for a, b, and c into the quadratic formula:
x = (-5 ± √(5^2 - 4 * 1 * -7)) / (2 * 1)
Step 5: Simplify the equation inside the square root:
x = (-5 ± √(25 + 28)) / 2
Step 6: Simplify further:
x = (-5 ± √(53)) / 2
Step 7: Compute the two possible solutions by evaluating the expression:
x1 = (-5 + √(53)) / 2
x2 = (-5 - √(53)) / 2
Therefore, the solutions to the equation x^2 + 5x - 7 = 0 using the quadratic formula are:
x1 ≈ 0.816
x2 ≈ -5.816