Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
x-(10*x^2-2)=0
Step-1 : Multiply the coefficient of the first term by the constant -10 • 2 = -20
Step-2 : Find two factors of -20 whose sum equals the coefficient of the middle term, which is 1 .
-20 + 1 = -19
-10 + 2 = -8
-5 + 4 = -1
-4 + 5 = 1 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and 5
-10x2 - 4x + 5x + 2
Step-4 : Add up the first 2 terms, pulling out like factors :
-2x • (5x+2)
Add up the last 2 terms, pulling out common factors :
1 • (5x+2)
Step-5 : Add up the four terms of step 4 :
(-2x+1) • (5x+2)
Solve : 5x+2 = 0
Subtract 2 from both sides of the equation :
5x = -2
Divide both sides of the equation by 5:
x = -2/5 = -0.400
Solve : -2x+1 = 0
Subtract 1 from both sides of the equation :
-2x = -1
Multiply both sides of the equation by (-1) : 2x = 1
Divide both sides of the equation by 2:
x = 1/2 = 0.500
Root plot for : y = -10x2+x+2
Axis of Symmetry (dashed) {x}={ 0.05}
Vertex at {x,y} = { 0.05, 2.02}
x -Intercepts (Roots) :
Root 1 at {x,y} = { 0.50, 0.00}
Root 2 at {x,y} = {-0.40, 0.00}