Solve the equation $4 x ^ { 2 } + \sqrt { 2 x + 1 } = \sqrt { 2 x + 5000 } .$ Restrict your attention to the horizontal span of 0 to 5.
A) 6.19
B) 4.11
C) 4.2
D) 5.51

Question

Quizplus · Accepted Answer

Squaring both sides of the equation gives $16 x ^ { 4 } + 8 x ^ { 3 } + 2 x ^ { 2 } + 2 x + 1 = 2 x + 5000$, which simplifies to $16 x ^ { 4 } + 8 x ^ { 3 } + 2 x ^ { 2 } - 4998 = 0$. Using a graphing calculator, we find that the only real solution in the interval [0, 5] is approximately 4.11.

Solve the Equation 4x2+2x+1=2x+5000.4 x ^ { 2 } + \sqrt { 2 x + 1 } = \sqrt { 2 x + 5000 } .4x2+2x+1​=2x+5000​.

Solve the Equation $4 x ^ { 2 } + \sqrt { 2 x + 1 } = \sqrt { 2 x + 5000 } .$