Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth. x^2-21=-4x
We rewrite the equation in standard form: x^2 + 4x - 21 = 0.
We can now use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
where a = 1, b = 4, and c = -21.
Substituting these values, we get:
x = (-4 ± √(4^2 - 4(1)(-21))) / 2(1)
x = (-4 ± √(16 + 84)) / 2
x = (-4 ± √100) / 2
We simplify the square root:
x = (-4 ± 10) / 2
There are two solutions:
x = (-4 + 10) / 2 = 3
x = (-4 - 10) / 2 = -7
Therefore, the solutions are x = 3 and x = -7.
To solve the quadratic equation x^2 - 21 = -4x using the quadratic formula, we first need to rewrite the equation in the standard form ax^2 + bx + c = 0.
In this case, we have x^2 + 4x - 21 = 0. Comparing this with the standard form, we find that a = 1, b = 4, and c = -21.
Now, let's substitute these values into the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values, we get:
x = (-4 ± √(4^2 - 4(1)(-21))) / (2(1))
Simplifying further, we have:
x = (-4 ± √(16 + 84)) / 2
x = (-4 ± √100) / 2
The square root of 100 is 10, so we have:
x = (-4 ± 10) / 2
Now, we will find the two possible solutions by separately solving for x when taking the positive and negative square roots:
1. For the positive square root:
x = (-4 + 10) / 2
x = 6 / 2
x = 3
2. For the negative square root:
x = (-4 - 10) / 2
x = -14 / 2
x = -7
Therefore, the solutions to the equation x^2 - 21 = -4x are x = 3 and x = -7.
To solve the quadratic equation x^2 - 21 = -4x using the quadratic formula, we first need to rearrange the equation so that it is in the general form ax^2 + bx + c = 0.
Rearrange the equation:
x^2 + 4x - 21 = 0
Now, we can identify the values of a, b, and c:
a = 1
b = 4
c = -21
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the values of a, b, and c into the formula:
x = (-(4) ± √((4)^2 - 4(1)(-21))) / (2(1))
Simplifying further:
x = (-4 ± √(16 + 84)) / 2
x = (-4 ± √(100)) / 2
x = (-4 ± 10) / 2
Now we have two possible solutions:
x1 = (-4 + 10) / 2 = 6 / 2 = 3
x2 = (-4 - 10) / 2 = -14 / 2 = -7
Therefore, the solutions to the equation x^2 - 21 = -4x, rounded to the nearest hundredth, are x = 3 and x = -7.