x ^ { 2 } + 5 x - 14 \quad \text { 2. } \quad 3 x ^ { 2 } + 20 x + 25
Evaluate
25+25x-83x^{2}
Factor
-83\left(x-\frac{25-5\sqrt{357}}{166}\right)\left(x-\frac{5\sqrt{357}+25}{166}\right)
Graph
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x^{2}+5x-28\times 3x^{2}+20x+25
Multiply 14 and 2 to get 28.
x^{2}+5x-84x^{2}+20x+25
Multiply 28 and 3 to get 84.
-83x^{2}+5x+20x+25
Combine x^{2} and -84x^{2} to get -83x^{2}.
-83x^{2}+25x+25
Combine 5x and 20x to get 25x.
factor(x^{2}+5x-28\times 3x^{2}+20x+25)
Multiply 14 and 2 to get 28.
factor(x^{2}+5x-84x^{2}+20x+25)
Multiply 28 and 3 to get 84.
factor(-83x^{2}+5x+20x+25)
Combine x^{2} and -84x^{2} to get -83x^{2}.
factor(-83x^{2}+25x+25)
Combine 5x and 20x to get 25x.
-83x^{2}+25x+25=0
Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.
x=\frac{-25±\sqrt{25^{2}-4\left(-83\right)\times 25}}{2\left(-83\right)}
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
x=\frac{-25±\sqrt{625-4\left(-83\right)\times 25}}{2\left(-83\right)}
Square 25.
x=\frac{-25±\sqrt{625+332\times 25}}{2\left(-83\right)}
Multiply -4 times -83.
x=\frac{-25±\sqrt{625+8300}}{2\left(-83\right)}
Multiply 332 times 25.
x=\frac{-25±\sqrt{8925}}{2\left(-83\right)}
Add 625 to 8300.
x=\frac{-25±5\sqrt{357}}{2\left(-83\right)}
Take the square root of 8925.
x=\frac{-25±5\sqrt{357}}{-166}
Multiply 2 times -83.
x=\frac{5\sqrt{357}-25}{-166}
Now solve the equation x=\frac{-25±5\sqrt{357}}{-166} when ± is plus. Add -25 to 5\sqrt{357}.
x=\frac{25-5\sqrt{357}}{166}
Divide -25+5\sqrt{357} by -166.
x=\frac{-5\sqrt{357}-25}{-166}
Now solve the equation x=\frac{-25±5\sqrt{357}}{-166} when ± is minus. Subtract 5\sqrt{357} from -25.
x=\frac{5\sqrt{357}+25}{166}
Divide -25-5\sqrt{357} by -166.
-83x^{2}+25x+25=-83\left(x-\frac{25-5\sqrt{357}}{166}\right)\left(x-\frac{5\sqrt{357}+25}{166}\right)
Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{25-5\sqrt{357}}{166} for x_{1} and \frac{25+5\sqrt{357}}{166} for x_{2}.
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