Solve the equation $\left| { x }^{ 2 }+4x+3 \right| = -\left( 2x+5 \right)$.
\({x}^{2}+4x+3=-(2x+5)\)
\({x}^{2}+4x+3=-2x-5\)
\({x}^{2}+4x+3+5=-2x-5+5\)
\({x}^{2}+4x+8=-2x \)
\(x^2+4x+8+2x=-2x+2x\)
\(x^2+6x+8=0\)
\(x_{1,\:2}=\frac{-6\pm \sqrt{6^2-4\cdot \:1\cdot \:8}}{2\cdot \:1}\)
\(\sqrt{6^2-4\cdot \:1\cdot \:8}=2 \)
\(x_{1,\:2}=\frac{-6\pm \:2}{2\cdot \:1}\)
\(x_1=\frac{-6+2}{2\cdot \:1},\:x_2=\frac{-6-2}{2\cdot \:1}\)
x=-2
x=-4
\({x}^{2}+4x+3=-(2x+5)\)
\({x}^{2}+4x+3=-2x-5\)
\({x}^{2}+4x+3+5=-2x-5+5\)
\({x}^{2}+4x+8=-2x \)
\(x^2+4x+8+2x=-2x+2x\)
\(x^2+6x+8=0\)
\(x_{1,\:2}=\frac{-6\pm \sqrt{6^2-4\cdot \:1\cdot \:8}}{2\cdot \:1}\)
\(\sqrt{6^2-4\cdot \:1\cdot \:8}=2 \)
\(x_{1,\:2}=\frac{-6\pm \:2}{2\cdot \:1}\)
\(x_1=\frac{-6+2}{2\cdot \:1},\:x_2=\frac{-6-2}{2\cdot \:1}\)
x=-2
x=-4
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