Use square roots to solve the following equation; round to the nearest hundredth.   5x^2 -526 =-651

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embizze eNotes educator| Certified Educator

Solve `5x^2-526=-651 ` :

To solve an equation in one variable where only one term contains the variable we usually isolate the variable by performing inverse operations in the reverse order of the usual order of operations -- thus you "undo" addition or subtraction, then "undo" multiplication or division, then "undo" exponents, etc...

At each step, we have an equation that is equivalent to the original equation in that the solution is still the same.

`5x^2-526=-651 ` Add 526 to both sides.

`5x^2=-125 ` Divide both sides by 5.

`x^2=-25 `

There are no real roots or solutions. By the fundamental theorem of algebra, there are two solutions. These solutions are in the complex numbers. In this case, both solutions are pure imaginary numbers which are complex conjugates of each other.

Taking the square root of both sides we get:

`x=+- sqrt(-25) `

So x is plus or minus 5i where i is the imaginary number and `i=sqrt(-1) `

iamkaori | Student

5x^2 - 526 = -651

Move the -526 over to get:

5x^2 = -651 - -526

= 5x^2 = -125

Divide both sides by 5:

x^2 = -25

Square root both sides, but look to see that the square becomes a negative number. Since squares cannot equal to a negative number, there is no solution.