How do you solve for x if x squared + x = 2 and x squared - 4 = 0?

Solve First Equation: Solve the first equation x squared + x = 2. Subtract 2 from both sides to set the equation to zero. x^2 + x - 2 = 0 Now, factor the quadratic equation. (x + 2)(x - 1) = 0 Set each factor equal to zero and solve for x. x + 2 = 0 or x - 1 = 0 x = -2 or x = 1Solve Second Equation: Solve the second equation x squared - 4 = 0. Factor the difference of squares. (x - 2)(x + 2) = 0 Set each factor equal to zero and solve for x. x - 2 = 0 or x + 2 = 0 x = 2 or x = -2Compare Solutions: Compare the solutions from both equations. From the first equation, we have x = -2 or x = 1. From the second equation, we have x = 2 or x = -2. The common solution between both equations is x = -2.

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How do you solve for $x$ if $x^2 + x = 2$ and $x^2 - 4 = 0$ ?

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Math Problems

Grade 8

Square roots of perfect squares

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Q. How do you solve for

x

x^2 + x = 2

and

x^2 - 4 = 0

Solve First Equation: Solve the first equation $x^2 + x = 2$ . $\newline$ Subtract $2$ from both sides to set the equation to zero. $\newline$ $x^2 + x - 2 = 0$ $\newline$ Now, factor the quadratic equation. $\newline$ $(x + 2)(x - 1) = 0$ $\newline$ Set each factor equal to zero and solve for $x$ . $\newline$ $x + 2 = 0$ or $x - 1 = 0$ $\newline$ $x = -2$ or $x = 1$
Solve Second Equation: Solve the second equation $x^2 - 4 = 0$ . Factor the difference of squares. $(x - 2)(x + 2) = 0$ Set each factor equal to zero and solve for $x$ . $x - 2 = 0$ or $x + 2 = 0$ $x = 2$ or $x = -2$
Compare Solutions: Compare the solutions from both equations. $\newline$ From the first equation, we have $x = -2$ or $x = 1$ . $\newline$ From the second equation, we have $x = 2$ or $x = -2$ . $\newline$ The common solution between both equations is $x = -2$ .