The solutions to the quadratic equation in the exact form are x = -1/2 or x = -5
Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
A quadratic equations can be split to several equations and it can be solved as a whole
In this case, the quadratic equation is given as
5x^2 + 11x + 2 = 0
Using the form of the quadratic equation y = ax^2 + bx + c, we have
a = 5, b = 11 and c = 2
The quadratic equation can be solved using the following formula
x = (-b ± √(b^2 - 4ac))/2a
Substitute the known values of a, b and c in the above equation
x = (-11 ± √(11^2 - 4 * 5 * 2))/2*2
Evaluate the exponent
x = (-11 ± √(121 - 4 * 5 * 2))/2*2
Evaluate the products
x = (-11 ± √(121 - 40))/4
Evaluate the sum
x = (-11 ± √(81))/4
Take the square root of 81
x = (-11 ± 9)/4
Expand
x = 1/4 * (-11 + 9) or x = 1/4 * (-11 - 9)
Evaluate the difference
x = 1/4 * -2 or x = 1/4 * -20
Evaluate the product
x = -1/2 or x = -5
Hence, the solutions to the quadratic equation in the exact form are x = -1/2 or x = -5
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