Solve for x 3-x^2=x-17

Problem

3−x2=x−17

Solution

1. Rearrange the equation into standard quadratic form a*x2+b*x+c=0 by moving all terms to one side.

3−x2−x+17=0

2. Combine the constant terms 3 and 17

−x2−x+20=0

3. Multiply the entire equation by −1 to make the leading coefficient positive.

x2+x−20=0

4. Factor the quadratic expression by finding two numbers that multiply to −20 and add to 1 These numbers are 5 and −4

(x+5)*(x−4)=0

5. Apply the zero product property by setting each factor equal to zero.

x+5=0

x−4=0

6. Solve for x in each linear equation.

x=−5

x=4

Final Answer

x=−5,4

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