The solutions to the quadratic equation [tex]\rm x^2 + 2x = 25[/tex] is [tex]-1\pm \sqrt{26 }[/tex].
Quadratics can be defined as a polynomial equation of a second degree, which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations.
The given equation is;
[tex]\rm x^2 + 2x = 25\\\\x^2+2x-25=0[/tex]
The solutions to the quadratic equation is determined by the following formula;
[tex]\rm x =\dfrac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex]
Where the value of a = 1, b = 2, and c = -25.
Substitute all the values in the formula;
[tex]\rm x =\dfrac{-b\pm \sqrt{b^2-4ac} }{2a}\\\\\rm x =\dfrac{-2\pm \sqrt{2^2-4\times 1\times (-25)} }{2\times 1}\\\\ x =\dfrac{-2\pm \sqrt{4+100} }{2}\\\\x =\dfrac{-2\pm \sqrt{104} }{2}\\\\x =\dfrac{-2\pm \sqrt{26 \times 2\times 2} }{2}\\\\x =\dfrac{-2\pm 2\sqrt{26 }}{2}\\\\x = 2 \times \dfrac{-1\pm \sqrt{26 }}{2}\\\\x=-1\pm \sqrt{26 }[/tex]
Hence, the solutions to the quadratic equation [tex]\rm x^2 + 2x = 25[/tex] is [tex]-1\pm \sqrt{26 }[/tex].
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