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x^{2}+2x-15=0
To solve the inequality, factor the left hand side. 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{-2±\sqrt{2^{2}-4\times 1\left(-15\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}. Substitute 1 for a, 2 for b, and -15 for c in the quadratic formula.
x=\frac{-2±8}{2}
Do the calculations.
x=3 x=-5
Solve the equation x=\frac{-2±8}{2} when ± is plus and when ± is minus.
\left(x-3\right)\left(x+5\right)\geq 0
Rewrite the inequality by using the obtained solutions.
x-3\leq 0 x+5\leq 0
For the product to be ≥0, x-3 and x+5 have to be both ≤0 or both ≥0. Consider the case when x-3 and x+5 are both ≤0.
x\leq -5
The solution satisfying both inequalities is x\leq -5.
x+5\geq 0 x-3\geq 0
Consider the case when x-3 and x+5 are both ≥0.
x\geq 3
The solution satisfying both inequalities is x\geq 3.
x\leq -5\text{; }x\geq 3
The final solution is the union of the obtained solutions.