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Using the quadratic formula to solve x2 + 20 = 2x, what are the values of x?
The quadratic formula is an effective way of solving quadratic equations especially when the splitting of the middle term is not feasible.
Answer: x = [ 2 ± √76 i ] / 2 are the solutions of the quadratic equation x2 + 20 = 2x.
Let us use the quadratic formula to solve x2 + 20 = 2x.
Explanation:
Let's write the equation in it's standard form
x2 + 20 = 2x
x2 - 2x + 20 = 0
a = 1, b = -2, c = 20 -------> when we compare with the standard form of a quadratic expression ax2 + bx + c = 0
By roots of quadratic equation formula,
x = [ -b ± √(b2 - 4ac) ] / 2a
x = [ -(-2) ± √{(-2)2 - 4(1)(20)} ] / 2(1)
x = [ 2 ± √{4 - 80} ] / 2
x = [ 2 ± √(-76) ] / 2
The value of x are : [ 2 + √(-76) ] / 2 and [ 2 - √(-76) ] / 2
Both the values of x are complex numbers.
Thus, the solutions of the quadratic expression x2 + 20 = 2x, using quadratic formula are x = [ 2 ± √76 i ] / 2.
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