Factor
2\left(x-\frac{-\sqrt{649}-7}{4}\right)\left(x-\frac{\sqrt{649}-7}{4}\right)
Evaluate
2x^{2}+7x-75
গ্রাফ
শেয়ার করুন
ক্লিপবোর্ডে কপি করা হয়েছে
2x^{2}+7x-75=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{-7±\sqrt{7^{2}-4\times 2\left(-75\right)}}{2\times 2}
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{-7±\sqrt{49-4\times 2\left(-75\right)}}{2\times 2}
Square 7.
x=\frac{-7±\sqrt{49-8\left(-75\right)}}{2\times 2}
Multiply -4 times 2.
x=\frac{-7±\sqrt{49+600}}{2\times 2}
Multiply -8 times -75.
x=\frac{-7±\sqrt{649}}{2\times 2}
Add 49 to 600.
x=\frac{-7±\sqrt{649}}{4}
Multiply 2 times 2.
x=\frac{\sqrt{649}-7}{4}
Now solve the equation x=\frac{-7±\sqrt{649}}{4} when ± is plus. Add -7 to \sqrt{649}.
x=\frac{-\sqrt{649}-7}{4}
Now solve the equation x=\frac{-7±\sqrt{649}}{4} when ± is minus. Subtract \sqrt{649} from -7.
2x^{2}+7x-75=2\left(x-\frac{\sqrt{649}-7}{4}\right)\left(x-\frac{-\sqrt{649}-7}{4}\right)
Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-7+\sqrt{649}}{4} for x_{1} and \frac{-7-\sqrt{649}}{4} for x_{2}.
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