10x2 - 64 = 36 + 6x2; whence,
4x2 - 100 = 0,
x2 = 25, and
x = ±5.
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There are no real solutions because the discriminant of the quadratic equation is less than zero.
It is a quadratic equation and its solutions can be found by using the quadratic equation formula.
10x2 - 64 = 36 + 6x2 Combine like terms: 4x2 = 100 Divide both sides by 4: x2 = 25 Take square roots: x = -5 or +5
is an equation of a line in plane coordinate geometry. The coordinates of every point on that line satisfy the equation so there are an infinite number of solutions to the equation.
Strictly speaking the above equation is a tautological equation or an IDENTITY. An identity is true for all values of any variables that appear in it. Thus, the above "equation" is true for all value of x. - that is, it has infinitely many solutions.