Solve the quadratic by factoring. 2x^(2)+5x=-2x-6 Answer: x=

Move Terms to One Side: Move all terms to one side of the equation to set the equation to zero. 2x^2 + 5x + 2x + 6 = 0 Combine like terms. 2x^2 + 7x + 6 = 0Combine Like Terms: Factor the quadratic equation. We need to find two numbers that multiply to 2*6=12 (a*c) and add up to 7 (b). The numbers 3 and 4 satisfy these conditions because 3*4=12 and 3+4=7. So we can write 7x as 3x + 4x. 2x^2 + 3x + 4x + 6 = 0Factor Quadratic Equation: Group the terms to factor by grouping. (2x^2 + 3x) + (4x + 6) = 0 Factor out the greatest common factor from each group. x(2x + 3) + 2(2x + 3) = 0Group Terms for Factoring: Factor out the common binomial factor. (x + 2)(2x + 3) = 0Factor Common Binomial: Set each factor equal to zero and solve for x. x + 2 = 0 or 2x + 3 = 0 x = -2 or x = -3/2

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Solve the quadratic by factoring.

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2 x^{2}+5 x=-2 x-6

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Answer:

x=

Move Terms to One Side: Move all terms to one side of the equation to set the equation to zero. $\newline$ $2x^2 + 5x + 2x + 6 = 0$ $\newline$ Combine like terms. $\newline$ $2x^2 + 7x + 6 = 0$
Combine Like Terms: Factor the quadratic equation. $\newline$ We need to find two numbers that multiply to $2\times 6=12$ ( $a\times c$ ) and add up to $7$ ( $b$ ). $\newline$ The numbers $3$ and $4$ satisfy these conditions because $3\times 4=12$ and $3+4=7$ . $\newline$ So we can write $7x$ as $3x + 4x$ . $\newline$ $a\times c$ $0$
Factor Quadratic Equation: Group the terms to factor by grouping. $\newline$ $(2x^2 + 3x) + (4x + 6) = 0$ $\newline$ Factor out the greatest common factor from each group. $\newline$ $x(2x + 3) + 2(2x + 3) = 0$
Group Terms for Factoring: Factor out the common binomial factor. $\newline$ $(x + 2)(2x + 3) = 0$
Factor Common Binomial: Set each factor equal to zero and solve for $x$ . $x + 2 = 0$ or $2x + 3 = 0$ $x = -2$ or $x = -\frac{3}{2}$