x-75+75=-x2

Move x2 to the left side of the equation by adding it to both sides.

x-75+75+x2=0

Combine fractions with similar denominators.

x-7+75+x2=0

Simplify by adding numbers.

Add -7 and 7.

x+05+x2=0

Add x and 0.

x5+x2=0

x5+x2=0

To write x5 as a fraction with a common denominator, multiply by 22.

x5⋅22+x2=0

To write x2 as a fraction with a common denominator, multiply by 55.

x5⋅22+x2⋅55=0

Write each expression with a common denominator of 10, by multiplying each by an appropriate factor of 1.

Multiply x5 and 22.

x⋅25⋅2+x2⋅55=0

Multiply 5 by 2.

x⋅210+x2⋅55=0

Multiply x2 and 55.

x⋅210+x⋅52⋅5=0

Multiply 2 by 5.

x⋅210+x⋅510=0

x⋅210+x⋅510=0

Combine the numerators over the common denominator.

x⋅2+x⋅510=0

Simplify the numerator.

Move 2 to the left of x.

2⋅x+x⋅510=0

Move 5 to the left of x.

2x+5⋅x10=0

Add 2x and 5x.

7×10=0

7×10=0

7×10=0

Since this is the only denominator in the list, the result is the LCD: 10.

10

Multiply each term in 7×10=0 by 10.

7×10⋅10=0⋅10

Cancel the common factor of 10.

Cancel the common factor.

7×10⋅10=0⋅10

Rewrite the expression.

7x=0⋅10

7x=0⋅10

Multiply 0 by 10.

7x=0

7x=0

Divide each term in 7x=0 by 7.

7×7=07

Cancel the common factor of 7.

Cancel the common factor.

7×7=07

Divide x by 1.

x=07

x=07

Divide 0 by 7.

x=0

x=0

Solve for x (x-7)/5+7/5=-x/2