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M2 Unit 3 Test Quadre
21.)
x^(2)+2x=-5

M $2$ Unit $3$ Test Quadre $\newline$ $21$ .) $\newline$ $x^{2}+2x=-5$

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Factor polynomials

Full solution

Q. M

2

Unit

3

Test Quadre

\newline

21

.)

\newline

x^{2}+2x=-5

Rearrange Equation: Step Title: Rearrange the Equation $\newline$ Concise Step Description: Move all terms to one side of the equation to set it equal to zero. $\newline$ Step Calculation: $x^2 + 2x + 5 = 0$ (originally given as $x^2 + 2x = -5$ , added $5$ to both sides) $\newline$ Step Output: $x^2 + 2x + 5 = 0$
Identify Coefficients: Step Title: Identify the Coefficients $\newline$ Concise Step Description: Identify the coefficients of the quadratic equation. $\newline$ Step Calculation: Coefficients are $1$ (for $x^2$ ), $2$ (for $x$ ), and $5$ (constant term). $\newline$ Step Output: Coefficients: $1$ , $2$ , $5$
Calculate Discriminant: Step Title: Calculate the Discriminant $\newline$ Concise Step Description: Use the discriminant formula $D = b^2 - 4ac$ to check if the roots are real and distinct, real and equal, or complex. $\newline$ Step Calculation: $D = (2)^2 - 4\cdot1\cdot5 = 4 - 20 = -16$ $\newline$ Step Output: Discriminant: $-16$
Conclusion on Roots: Step Title: Conclusion on Roots $\newline$ Concise Step Description: Since the discriminant is negative, the quadratic equation has complex roots and cannot be factored using real numbers. $\newline$ Step Calculation: No real factors exist because the discriminant is less than zero. $\newline$ Step Output: No real factoring possible.

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