Today's soundtrack is Dissection: Storm of the Light's Bane/Where Dead Angels Lie, a classic black metal album.
This morning, I'm putting together the past few lessons about radicals - absolute value, simplifying radical expressions, adding and subtracting radical expressions, and multiplying and dividing radical expressions - and now I'm learning how to solve radical linear equations.
Important note: if our solution to a linear equation does not fit within the variable's possible values, it is an extraneous root and no real solution exists.
If we are given a linear equation with a single radical, the steps to solve are as follows:
1) Determine what the variable's value is defined at (x≥0, x≤0, or x∈ℝ)
2) Isolate the radicand
3) Raise both sides of the equation to an exponent equal to the index of the radical
4) Verify the solution to verify that a real root exists within the variable's possible values
To solve a linear equation with two variable radicals, we:
1) Determine what the variable's value is defined at (x≥0, x≤0, or x∈ℝ)
2) Find like terms
3) Balance both sides of the equation while isolating x
4) Verify the solution to verify that a real root exists within the variable's possible values