Solve the equation. sqrt (5x+60)-7=2x-13

1. Isolate the square root<br /> Add 7 to both sides: $\sqrt{5x + 60} = 2x - 6$.<br />2. Square both sides<br /> Square both sides to eliminate the square root: $5x + 60 = (2x - 6)^2$.<br />3. Expand and simplify<br /> Expand the right side: $5x + 60 = 4x^2 - 24x + 36$.<br />4. Rearrange into a quadratic equation<br /> Move all terms to one side: $4x^2 - 29x - 24 = 0$.<br />5. Solve the quadratic equation<br /> Use the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ with $a = 4$, $b = -29$, $c = -24$.<br /> Calculate discriminant: $(-29)^2 - 4 \cdot 4 \cdot (-24) = 841$.<br /> Find roots: $x = \frac{29 \pm \sqrt{841}}{8}$.<br /> Simplify: $x = \frac{29 \pm 29}{8}$.<br /> Solutions: $x = \frac{58}{8} = 7.25$ and $x = \frac{0}{8} = 0$.<br />6. Verify solutions<br /> Check $x = 7.25$: $\sqrt{5(7.25) + 60} - 7 = 2(7.25) - 13$; true.<br /> Check $x = 0$: $\sqrt{5(0) + 60} - 7 = 2(0) - 13$; false.