can you solve the equation using the quadratic formula x2 + 3x = 7? Explain and provide an exact answer.
x^2 + 3x - 7 = 0
a=1, b=3, c=-7
x = (-3 ± √37)/2
Yes, I can help you solve the equation using the quadratic formula.
First, let's rewrite the equation in the standard form: x^2 + 3x - 7 = 0.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a),
where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c = 0.
In our equation, a = 1, b = 3, and c = -7.
Plugging these values into the quadratic formula, we get:
x = (-3 ± √(3^2 - 4(1)(-7))) / (2(1)).
Simplifying further:
x = (-3 ± √(9 + 28)) / 2,
x = (-3 ± √37) / 2.
So, the two solutions to the equation x^2 + 3x - 7 = 0 are:
x = (-3 + √37) / 2 and x = (-3 - √37) / 2.
These are the exact answers to the quadratic equation.