Solve for x. 4x^(2)+52=-8x

Move to Standard Form: Write the equation in standard form by moving all terms to one side of the equation. 4x^2 + 52 = -8x Add 8x to both sides to get: 4x^2 + 8x + 52 = 0Factor or Use Quadratic Formula: Factor the quadratic equation if possible. The quadratic equation 4x^2 + 8x + 52 does not factor nicely, so we will use the quadratic formula to find the solutions for x. The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a), where a = 4, b = 8, and c = 52.Calculate Discriminant: Calculate the discriminant to determine the nature of the roots. The discriminant is given by b^2 - 4ac. Let's calculate it: Discriminant = (8)^2 - 4(4)(52) Discriminant = 64 - 832 Discriminant = -768 Since the discriminant is negative, there are no real solutions to the equation, only complex solutions.Calculate Complex Solutions: Since the discriminant is negative, calculate the complex solutions using the quadratic formula. x = (-8 ± √(-768)) / (8) We can simplify √(-768) as √(768) * i, where i is the imaginary unit.Simplify Solutions: Simplify the solutions. x = (-8 ± √(768) * i) / 8 x = (-8 ± 8√(3) * i) / 8 x = -1 ± √(3) * i

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Solve for $x$ . $\newline$ $4 x^{2}+52=-8 x$

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\newline

4 x^{2}+52=-8 x

Move to Standard Form: Write the equation in standard form by moving all terms to one side of the equation. $\newline$ $4x^2 + 52 = -8x$ $\newline$ Add $8x$ to both sides to get: $\newline$ $4x^2 + 8x + 52 = 0$
Factor or Use Quadratic Formula: Factor the quadratic equation if possible. $\newline$ The quadratic equation $4x^2 + 8x + 52$ does not factor nicely, so we will use the quadratic formula to find the solutions for $x$ . The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ , where $a = 4$ , $b = 8$ , and $c = 52$ .
Calculate Discriminant: Calculate the discriminant to determine the nature of the roots. $\newline$ The discriminant is given by $b^2 - 4ac$ . Let's calculate it: $\newline$ Discriminant = $(8)^2 - 4(4)(52)$ $\newline$ Discriminant = $64 - 832$ $\newline$ Discriminant = $-768$ $\newline$ Since the discriminant is negative, there are no real solutions to the equation, only complex solutions.
Calculate Complex Solutions: Since the discriminant is negative, calculate the complex solutions using the quadratic formula. $\newline$ $x = \frac{-8 \pm \sqrt{-768}}{8}$ $\newline$ We can simplify $\sqrt{-768}$ as $\sqrt{768} \cdot i$ , where $i$ is the imaginary unit.
Simplify Solutions: Simplify the solutions. $\newline$ $x = \frac{-8 \pm \sqrt{768} \cdot i}{8}$ $\newline$ $x = \frac{-8 \pm 8\sqrt{3} \cdot i}{8}$ $\newline$ $x = -1 \pm \sqrt{3} \cdot i$