Answer:
Raise both sides of the equation to the power of 2
Raise both sides of the equation to the power of 2 again
Simplify to get a quadratic equation.
Use the quadratic formula to find the values of x.
Step-by-step explanation:
The radical equation is expressed as:
[tex]\sqrt{x+3} - \sqrt{2x-1} = -2[/tex]
The following steps are to be followed to calculate x:
Step 1: Raise both sides of the equation to the power of 2.
[tex](\sqrt{x+3} - \sqrt{2x-1})^2 = (-2)^2\\x+3 - 2\sqrt{x+3}\sqrt{2x-1}+(2x-1) = 4\\ - 2\sqrt{x+3}\sqrt{2x-1}+x+3+2x-1 = 4\\ - 2\sqrt{x+3}\sqrt{2x-1}+3x+2 = 4\\ - 2\sqrt{x+3}\sqrt{2x-1} +3x-2 = 0\\[/tex]
Step 2: Raise both sides of the equation to the power of 2 again
[tex](-2\sqrt{x+3}\sqrt{2x-1})^2 = (2-3x)^2\\4(x+3)(2x-1) = (2-3x)^2\\[/tex]
Step 3: Simplify to get a quadratic equation.
[tex]\\4(2x^2-x+6x-3) = 4-12x+9x^2\\4(2x^2+5x-3) = 4-12x+9x^2\\8x^2+20x-12 = 4-12x+9x^2\\x^2-32x+16 = 0[/tex]
Step 4: Use the quadratic formula to find the values of x.
x = 32±√32²-4(16)/2
