How do you solve (−2x+5)2=−8?

2 Answers
smendyka
Jul 29, 2017

See a solution process below:

Explanation:

First, expand the term on the left using this special rule for multiplying quadratics:

(x+y)2=x2+2xy+y2

Substituting gives:

(−2x+5)2=−8

(−2x)2+(2⋅−2x⋅5)+52=−8

4x2+(−20x)+25=−8

4x2−20x+25=−8

We can next convert this to standard form:

4x2−20x+25+8=−8+8

4x2−20x+33=0

We can now use the quadratic formula to find the solutions for x. The quadratic formula states:

For ax2+bx+c=0, the values of x which are the solutions to the equation are given by:

x=−b±√b2−(4ac)2⋅a

Substituting:

4 for a

−20 for b

33 for c gives:

x=−(−20)±√−202−(4⋅4⋅33)2⋅4

x=20±√400−5288

x=20±√−1288

x=20±√64⋅−28

x=20±√64√−28

x=20±8√−28

Or

x=208±8√−28

x=52±√−2

Alan P.
Jul 29, 2017

No Real solutions;
within Complex numbers: x=25−√2i or 25+√2i

Explanation:

Given
xxx(−2x+5)2=−8

We note that any Real value squared must be ≥0
therefore this equation has No valid Real solutions

If we are dealing with Complex values, then
xxx(−2x+5)2=−8

xxx4x2−20x+25=−8

xxx4x2−20x+33=0

Then applying the quadratic formula that tells us that an equation of the form: ax2+bx+c=0
has solutions:
xxxx=−b±√b2−4ac2a

We have solutions:
xxxx=20±√400−4⋅4⋅332⋅4

xxx=20±√−1288

xxx=20±8√2i8

xxx=52±√2i

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