What is the solution to the equation square root of w squared plus 7 w minus 39 end root is equal to square root of 10 w plus 1 end root ?

Since both sides are square roots, set the expressions inside them equal: w² + 7w − 39 = 10w + 1. Rearranging gives w² − 3w − 40 = 0, which factors as (w − 8)(w + 5) = 0, so the candidates are w = 8 and w = −5. For w = −5, the radicands are negative, so it is not allowed; w = 8 makes both radicands 81. The solution is w = 8.

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