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givi [52]
3 years ago
5

Solve the equation x+x(2x-5)=23

Mathematics
2 answers:
andriy [413]3 years ago
8 0

Answer:

\large\boxed{1\pm2.5\sqrt2}

Step-by-step explanation:

x+x(2x-5)=23\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\x+2x^2-5x=23\qquad\text{combine like terms}\\\\2x^2+(x-5x)=23\\\\2x^2-4x=23\qquad\text{subtract 23 from both sides}\\\\2x^2-4x-23=0\\\\\text{use the quadratic formula for a quadratic trinomial:}\ ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\a=2,\ b=-4,\ c=-23\\\\x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4(2)(-23)}}{2(2)}=\dfrac{4\pm\sqrt{200}}{4}=\dfrac{4\pm\sqrt{100\cdot2}}{4}

=\dfrac{4\pm\sqrt{100}\cdot\sqrt2}{4}=\dfrac{4\pm10\sqrt2}{4}=1\pm2.5\sqrt2

VARVARA [1.3K]3 years ago
3 0
My guess is 2+5(square of 2)/ 2 and 2-5(square of 2)/2
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