Solve for x 2x^2+16<8x

Problem

2*x2+16<8*x

Solution

1. Rearrange the inequality into standard quadratic form by subtracting 8*x from both sides.

2*x2−8*x+16<0

2. Simplify the expression by dividing the entire inequality by the common factor 2

x2−4*x+8<0

3. Identify the properties of the quadratic function ƒ(x)=x2−4*x+8 by calculating the discriminant D=b2−4*a*c

D=(−4)2−4*(1)*(8)

D=16−32

D=−16

4. Analyze the result. Since the discriminant is negative (D<0 and the leading coefficient is positive (1>0, the parabola y=x2−4*x+8 opens upward and never touches or crosses the xaxis.

5. Conclude that the expression x2−4*x+8 is always positive for all real values of x Therefore, there are no values of x that make the expression less than zero.

Final Answer

2*x2+16<8*x⇒No real solution

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