The solutions to the quadratic equation of the sprinkler in the exact form are x = 7 + 2√110 and x = 7 - 2√110
<h3>What are
quadratic equations?</h3>
Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
<h3>How to determine the solution to the
quadratic equation?</h3>
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
-x^2 + 14x + 61 = 0
Using the form of the quadratic equation y = ax^2 + bx + c, we have
a = -1, b = 14 and c = 61
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 = (-14 ± √(14^2 - 4*-1*61))/2*-1
Evaluate the exponent
x = (-14 ± √(196 - 4*-1*61))/2*-1
Evaluate the products
x = (-14 ± √(196 + 244))/-2
Evaluate the sum
x = (-14 ± √(440))/-2
Express 440 as 4 * 110
x = (-14 ± √(4 * 110))/-2
Take the square root of 4
x = (-14 ± 2√110)/-2
Evaluate the quotient
x = 7 ± 2√110
Split the equation
x = 7 + 2√110 and x = 7 - 2√110
Hence, the solutions to the quadratic equation of the sprinkler in the exact form are x = 7 + 2√110 and x = 7 - 2√110
Read more about quadratic equations at
brainly.com/question/1214333
#SPJ1
