Prove the trigonometric identity $\left(5\sin\left(x\right)+5\cos\left(x\right)\right)^2=25+25\sin\left(2x\right)$

 Main Topic: Discriminant of Quadratic Equation

Quadratic equations are those algebraic equations of the form ax^2+bx+c, where a, b, and c are constant values. The discriminant of a quadratic equation is calculated using the formula D=b^2-4ac, and it helps us to determine how many roots an equation of this type has. When D>0 the equation has two real roots, when D<0 the equation has no real roots, and when D=0 the equation has a repeated real root.