solve 7x^2 = 2x+3
Please show all work
7x^2 = 2x + 3
7x^2 - 2x - 3 = 0
Use the quadratic formula to solve for x.
-b ± √(b^2 - 4ac)
x = -------------------------
2a
a, b and c are the constants in the equation.
-(-2) ± √((-2)^2 - 4(7)(-3))
x = -----------------------------------
2(7)
2 ± √(4 + 84)
x = --------------------
14
2 ± √88
x = --------------
14
2 ± 9.38
x = --------------
14
2 + 9.38 2 - 9.38
x = -------------- and x = --------------
14 14
2 + 9.38 2 - 9.38
x = -------------- and x = --------------
14 14
x = 0.8129 and x = -0.5271
Check both values.
7x^2 = 2x + 3
7(0.8129)^2 = 2(0.8129) + 3
7(.6608) = 1.6258 + 3
4.6256 = 4.6258
With rounding errors, that is acceptable.
7x^2 = 2x + 3
7(-0.5271)^2 = 2(-0.5271) + 3
7(0.2778) = -1.0542 + 3
1.9446 = 1.9458
Again, rounding errors account for the minor difference.