To rewrite the equation $2(x^2 + x) = 5$ in the standard form $ax^2 + bx + c = 0$, follow these steps:

Step 1: Expand and Distribute

Distribute the 2 across the terms inside the parentheses: $2(x^2 + x) = 2x^2 + 2x$ So, the equation becomes: $2x^2 + 2x = 5$

Step 2: Move All Terms to One Side

Subtract 5 from both sides to set the equation equal to 0: $2x^2 + 2x - 5 = 0$

Step 3: Identify the Coefficients

Now the equation is in the standard form $ax^2 + bx + c = 0$, where:

• $a = 2$
• $b = 2$
• $c = -5$

So, the equation in standard form is: $2x^2 + 2x - 5 = 0$

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Related Questions

1. How can you solve the quadratic equation $2x^2 + 2x - 5 = 0$?
2. What are the methods to factorize quadratic equations?
3. How do you calculate the roots of a quadratic equation using the quadratic formula?
4. What is the significance of the discriminant in solving quadratic equations?
5. How do you complete the square for the equation $2x^2 + 2x - 5 = 0$?
6. How can you graph the quadratic equation $2x^2 + 2x - 5 = 0$?
7. What are the axis of symmetry and vertex of the quadratic equation?
8. Can you solve a quadratic equation by substitution or elimination methods?

Tip

When moving all terms to one side, always ensure the quadratic equation is set to zero; this is key for applying various solving methods.