# Solve for x -1/2x^2+5x=8

Solve for x -1/2x^2+5x=8
Combine and .
Multiply each term in by to eliminate the fractions.
Multiply each term in by .
Simplify the left side.
Simplify each term.
Cancel the common factor of .
Move the leading negative in into the numerator.
Cancel the common factor.
Rewrite the expression.
Multiply by .
Simplify the right side.
Multiply by .
Subtract from both sides of the equation.
Factor the left side of the equation.
Factor out of .
Factor out of .
Factor out of .
Rewrite as .
Factor out of .
Factor out of .
Factor.
Factor using the AC method.
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Write the factored form using these integers.
Remove unnecessary parentheses.
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set equal to and solve for .
Set equal to .
Add to both sides of the equation.
Set equal to and solve for .
Set equal to .
Add to both sides of the equation.
The final solution is all the values that make true.
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