Answer:
[tex]x=-4+\sqrt{2}[/tex]
[tex]x=-4-\sqrt{2}[/tex]
Step-by-step explanation:
The quadratic formula is an equation that can be used to find the roots of a quadratic equation when one is given the equation in standard form. A quadratic equation in standard form is the following,
[tex]ax^2 +bx + c=0[/tex]
The quadratic formula is the following,
[tex]\frac{(-a)(+-)\sqrt{(x)^2-4(b)(c)}}{2(a)}[/tex]
Substitute in the given coefficients for the following equation,
[tex]2x^2 + 16x + 28 = 0[/tex]
Substitute,
[tex]\frac{-16(+-)\sqrt{(16)^2-4(2)(8)}}{2(2)}[/tex]
Simplify,
[tex]\frac{-16(+-)\sqrt{256-224}}{4}\\\\=\frac{-16(+-)\sqrt{32}}{4}\\\\=\frac{-16(+-)4\sqrt{2}}{4}\\\\=-4(+-)\sqrt{2}[/tex]
The roots of the quadratic equation ([tex]2x^2+16x+28=0[/tex]) are ([tex]x=-4+\sqrt2[/tex]) and ([tex]x=-4-\sqrt{2}[/tex])
