Solve the following equation using the quadratic formula.
x^2 + 12x+35=0
To solve the equation using the quadratic formula, we start by identifying the values of a, b, and c in the equation ax^2 + bx + c = 0.
In this case, a = 1, b = 12, and c = 35.
Using the quadratic formula x = (-b ± √(b^2 - 4ac)) / 2a, we can substitute the values into the formula:
x = (-(12) ± √((12)^2 - 4(1)(35))) / (2(1))
Simplifying further:
x = (-12 ± √(144 - 140)) / 2
x = (-12 ± √4) / 2
x = (-12 ± 2) / 2
The two possible solutions are:
x = (-12 + 2) / 2 = -10 / 2 = -5
x = (-12 - 2) / 2 = -14 / 2 = -7
Therefore, the solutions to the equation x^2 + 12x + 35 = 0 are x = -5 and x = -7.
To solve the equation x^2 + 12x + 35 = 0 using the quadratic formula, we can use the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
where a, b, and c correspond to the coefficients in the equation.
In this equation, a = 1, b = 12, and c = 35.
Now we substitute these values into the quadratic formula:
x = (-12 ± √(12^2 - 4 * 1 * 35)) / (2 * 1)
Simplifying further:
x = (-12 ± √(144 - 140)) / 2
x = (-12 ± √4) / 2
Now, we can simplify the square root:
x = (-12 ± 2) / 2
This gives us two possible solutions:
x1 = (-12 + 2) / 2 = -5
x2 = (-12 - 2) / 2 = -7
Therefore, the solutions to the equation x^2 + 12x + 35 = 0 are x = -5 and x = -7.
To solve the given quadratic equation using the quadratic formula, we first need to identify the coefficients a, b, and c in the general form of a quadratic equation:
ax^2 + bx + c = 0
In our case, the equation is x^2 + 12x + 35 = 0.
Comparing this equation with the general form, we can determine that a = 1, b = 12, and c = 35.
Now, we can substitute these values into the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in our values, we get:
x = ( -12 ± √(12^2 - 4(1)(35))) / (2(1))
Simplifying further:
x = (-12 ± √(144 - 140)) / 2
x = (-12 ± √4) / 2
x = (-12 ± 2) / 2
Therefore, the solutions for the equation x^2 + 12x + 35 = 0 are:
x1 = (-12 + 2) / 2 = -5
x2 = (-12 - 2) / 2 = -7
So the two solutions to the equation are x = -5 and x = -7.