Answer (if we're solving for x):
[tex]x=-7[/tex] or [tex]\frac{9}{2}[/tex]
Step-by-step explanation:
- Rearrange the terms from [tex]2x^{2} =63-5x[/tex] to [tex]2x^{2}=-5x+63[/tex]
- Move the terms to the left side: [tex]2x^{2}-(-5x+63)=0[/tex]
- Use the "sum-product" pattern: [tex]2x^2+14x-9x-63=0[/tex]
- Get the common factor drom the 2 pairs:[tex]2x(x+7)-9(x+7)=0[/tex]
- Rewrite the equation in factored form as [tex](2x-9)(x+7)=0[/tex]
- Create 2 equations from [tex](2x-9)(x+7)=0[/tex]: [tex]2x-9=0\\x+7=0[/tex]
- This means that [tex]x[/tex] can either be [tex]-7 (-7+7=0=x+7)[/tex] or [tex]\frac{9}{2} (\frac{8}{2}=4; \frac{9}{2}=4.5)[/tex]
