Solve this quadratic equation using the quadratic formula.
x^2 + 8x - 5 = 0
To solve a quadratic equation using the quadratic formula, we can follow these steps:
Step 1: Identify the coefficients of the quadratic equation.
The given equation is x^2 + 8x - 5 = 0. Here, the coefficient of x^2 is 1, the coefficient of x is 8, and the constant term is -5.
Step 2: Substitute the coefficients into the quadratic formula.
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 case, a = 1, b = 8, and c = -5. Substituting these values into the quadratic formula, we have:
x = (-8 ± √(8^2 - 4*1*(-5))) / (2*1)
Step 3: Simplify the equation and find the solutions.
Calculating the values inside the square root:
x = (-8 ± √(64 + 20)) / 2
x = (-8 ± √84) / 2
Simplifying the square root:
x = (-8 ± √(4 * 21)) / 2
x = (-8 ± 2√21) / 2
Now, we can simplify further by canceling out the common factor of 2 in the numerator and denominator:
x = -4 ± √21
Therefore, the solutions to the quadratic equation x^2 + 8x - 5 = 0 are:
x = -4 + √21
x = -4 - √21
Have you learned the formula? Can you plug in a, b and c? It's time you did.
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