Answer:
2x^{2} + 2x - 56 = x^{2} + x\\
x_1 = -8
x_2 = 7
x^{2} -9x= x- 9\\
x_1 = 1
x_2 = 9
Step-by-step explanation:
2x^{2} + 2x - 56 = x^{2} + x\\
2x^{2} + 2x - 56 - x^{2} - x\\
x^{2} + x - 56 = 0\\
x_1,2 = (-b ± √(b^2-4 ac))/2a
a = 1, b = 1, c = -56
x_1,2 = (-1 ± √(1^2-4*1* (-56)))/(2*1)
x_1 = (-1- √(1^2-4*1* (-56)))/(2*1)
x_1 = (-1- √(1^2-4*1* (-56)))/(2*1)= -8
x_2 = (-1+ √(1^2-4*1* (-56)))/(2*1)= 7
Proof
2*(-8)^{2} + 2*(-8)- 56 =(-〖8)〗^{2} +(-8)\\
128- 16- 56 = 64- 8\\
56 = 56\\
2*(7)^{2} + 2*7 - 56 =(7)^{2} + 7\\
98+ 14 - 56 =49 + 7\\
98+ 14 - 56 =49 + 7\\
56 =56\\
x^{2} -9x= x- 9\\
x^{2} -9x= x- 9\\
x^2-x-9x+9=0
x^2-10x+9=0
x_1,2 = (-b ± √(b^2-4 ac))/2a
a = 1, b = -10, c = 9
x_1,2 = (-(-10) ± √(〖(-10)〗^2-4* 1*9))/(2*1)
x_1 = (10-8)/2=1
x_2 = (10+8)/2=9
Proof
x^{2} -9x= x- 9\\
1^{2} -9*1= 1- 9\\
-8= - 8\\
9^{2} -9*9= 9- 9\\
0= 0\\
