What are the solutions to the equation x^2-8x=24
Mathematics · High School · Tue Nov 03 2020
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Given the quadratic equation:
x^2 - 8x = 24
Can be written as;
x^2 - 8x - 24 = 0
Determine the solutions:
Solution:
In order to determine the solution of the given quadratic equation, we must think of a number, that when multiplied the product will be the last term and when added the sum will be the second term. If we cannot find the value of the number then we will use the quadratic equation.
Quadratic Equation:
x = −b ± √(b^2 − 4ac)/2a
a = 1 b = -8 c = -24
Substitute the given values of a, b and c to the equation.
x = −(-8) ± √((-8)^2 − 4(1)(-24))/2(1)
x = 8 ± √(64 +96)/2
x = 8 ± √160/2
x = 8 ± 12.65/2
Solve separately.
x = 8 + 12.65/2
x = 20.65/2
x = 10.33
x = 8 -12.65/2
x = -4.65/2
x = -2.33
Final answer:
The solutions in the given quadratic equation are: x = 10.33 and x = -2.33