Answer:
x = ( √11 + 5 ) / 2, and x = ( - √11 + 5 ) / 2
Step-by-step explanation:
Let us solve by completing the square;
7 = - 2x^2 + 10x, ⇒ Switch sides,
- 2x^2 + 10x = 7, ⇒ Divide both sides by - 2,
x^2 - 5x = - 7 / 2, ⇒ Write the equation in the form x^2 + 2ax+ a^2, ( x + a )^2, solving for the value of a,
2ax = - 5x,
a = - 5x / 2x,
a = - 5 / 2, ⇒ Add a^2 ⇒ ( - 5 / 2 )^2 to either side of equation,
x^2 - 5x + ( - 5 / 2 )^2 = - 7 / 2 + ( - 5 / 2 )^2, ⇒ Simplify,
( x - 5 / 2 )^2 = 11 / 4,
| x - 5 / 2 | = √ ( 11 / 4 ), Solve for value( s ) of x,
Answer; x = ( √11 + 5 ) / 2, and x = ( - √11 + 5 ) / 2
