use the quadratic formula.
2x2 + 8x = - 1
put it in standard format:
2x2 + 8x + 1=0
x= (-8 +-sqrt(64-8))/4
you do it.
to indicate exponents on this forum we usually say ..
2x^2 + 8x = - 1
2x^2 + 8x + 1 = 0
here a=2, b=8, c=1
and
x =(-b ± √(b^2 - 4ac))/(2a)
= (-8 ± √(64-8))/4
= (-4 ± √14)/2
2X2+8x=-1
4+8x=-1
8x=-1-4
x=-5/8
x=-0.625
To solve the quadratic equation 2x^2 + 8x = -1 using the quadratic formula, we first need to identify the coefficients of the quadratic equation. The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c represent the coefficients.
In this case, the equation is 2x^2 + 8x = -1. We can rewrite it as 2x^2 + 8x + 1 = 0 by moving the constant term (-1) to the other side of the equation.
Now, let's apply the quadratic formula to solve for x:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our equation, a = 2, b = 8, and c = 1. Substituting these values into the formula, we get:
x = (-8 ± √(8^2 - 4 * 2 * 1)) / (2 * 2)
Simplifying further:
x = (-8 ± √(64 - 8)) / 4
x = (-8 ± √56) / 4
Now, we have two possibilities because of the ± sign. To find both values of x, we evaluate the positive and negative cases separately:
For the positive case:
x = (-8 + √56) / 4
x = (-8 + 2√14) / 4
Simplifying:
x = -2 + (√14 / 2)
For the negative case:
x = (-8 - √56) / 4
x = (-8 - 2√14) / 4
Simplifying:
x = -2 - (√14 / 2)
So, the solutions to the quadratic equation 2x^2 + 8x = -1 are:
x = -2 + (√14 / 2)
x = -2 - (√14 / 2)