Solve the following quadratic equations by extracting square roots
Answer (1)
To solve the equations by extracting square roots, follow these steps:1.[tex]x^2 - 144 = 0[/tex]Add 144 to both sides:[tex] x^2 = 144[/tex]Take the square root of both sides:[tex]x = \pm \sqrt{144}[/tex][tex]x = \pm 12[/tex]Solutions: x = 12 and x = -122.[tex]x^2 = 18[/tex]Take the square root of both sides: [tex]x = \pm \sqrt{18}[/tex]Simplify: [tex]\sqrt{18}[/tex] [tex]\sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}[/tex][tex]x = \pm 3\sqrt{2}[/tex] Solutions: [tex]x = 3\sqrt{2} \: and \: x = -3\sqrt{2}[/tex]3.[tex](x - 5)^2 = 49[/tex]Take the square root of both sides: [tex]x - 5 = \pm \sqrt{49}[/tex][tex]x - 5 = \pm 7[/tex]Solve for ( x ): [tex]x - 5 = 7[/tex][tex]x = 12[/tex][tex]x - 5 = -7[/tex][tex]\[ x = -2[/tex]Solutions: x = 12 and x = -2 CARRY ON LEARNING!
