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factor(x^{2}+x-7)
Subtract 4 from -3 to get -7.
x^{2}+x-7=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{-1±\sqrt{1^{2}-4\left(-7\right)}}{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{-1±\sqrt{1-4\left(-7\right)}}{2}
Square 1.
x=\frac{-1±\sqrt{1+28}}{2}
Multiply -4 times -7.
x=\frac{-1±\sqrt{29}}{2}
Add 1 to 28.
x=\frac{\sqrt{29}-1}{2}
Now solve the equation x=\frac{-1±\sqrt{29}}{2} when ± is plus. Add -1 to \sqrt{29}.
x=\frac{-\sqrt{29}-1}{2}
Now solve the equation x=\frac{-1±\sqrt{29}}{2} when ± is minus. Subtract \sqrt{29} from -1.
x^{2}+x-7=\left(x-\frac{\sqrt{29}-1}{2}\right)\left(x-\frac{-\sqrt{29}-1}{2}\right)
Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-1+\sqrt{29}}{2} for x_{1} and \frac{-1-\sqrt{29}}{2} for x_{2}.
x^{2}+x-7
Subtract 4 from -3 to get -7.