Find all solutions of the equation and express them in the form a+bi
X^2+12x+37=0
To find the solutions of the equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)
In this case, a = 1, b = 12, and c = 37. Plugging these values into the quadratic formula, we have:
x = (-12 ± √(12^2 - 4(1)(37)))/(2(1))
x = (-12 ± √(144 - 148))/(2)
x = (-12 ± √(-4))/(2)
x = (-12 ± 2i)/(2)
x = -6 ± i
So, the solutions to the equation x^2 + 12x + 37 = 0 can be expressed as -6 + i and -6 - i.
To find the solutions of the equation x^2 + 12x + 37 = 0 and express them in the form a+bi, you can use the quadratic formula.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a = 1, b = 12, and c = 37. Plugging these values into the quadratic formula, we have:
x = (-(12) ± √((12)^2 - 4(1)(37))) / (2(1))
Simplifying further:
x = (-12 ± √(144 - 148)) / 2
x = (-12 ± √(-4)) / 2
x = (-12 ± 2i) / 2
Now we can simplify the expression by dividing both the numerator and denominator by 2:
x = -12/2 ± 2i/2
x = -6 ± i
Therefore, the solutions of the equation x^2 + 12x + 37 = 0, expressed in the form a+bi, are:
x = -6 + i
x = -6 - i
To find the solutions of the quadratic equation x^2 + 12x + 37 = 0, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a),
where a, b, and c are the coefficients of the quadratic equation.
In this case, a = 1, b = 12, and c = 37. Substituting these values into the quadratic formula, we have:
x = (-12 ± √(12^2 - 4*1*37)) / (2*1)
= (-12 ± √(144 - 148)) / 2
= (-12 ± √(-4)) / 2.
Since there is a square root of a negative number, we can rewrite it using the imaginary unit i, where i^2 = -1.
x = (-12 ± 2i) / 2
= -6 ± i.
Therefore, the solutions of the equation x^2 + 12x + 37 = 0 can be written as:
x = -6 + i and x = -6 - i.