Solve for 'a' in the Quadratic Equation: 4x² = -4x + 16

Q: Why do I need to rearrange to standard form first?

The standard form $ ax^2 + bx + c = 0 $ is the universal format for identifying coefficients. Without rearranging, you might miss terms or get confused about signs!

Q: What if the equation is already equal to zero?

Lucky you! If it's already in the form $ ax^2 + bx + c = 0 $, you can immediately identify the coefficients without rearranging.

Q: How do I handle the negative signs when rearranging?

When moving terms across the equals sign, flip their signs. So $ -4x $ becomes $ +4x $ and $ +16 $ becomes $ -16 $.

Q: What are the b and c values in this equation?

From $ 4x^2 + 4x - 16 = 0 $: b = 4 (coefficient of x) and c = -16 (constant term). Remember to include the signs!

Quadratic Coefficients with Standard Form

What is the value of $a$ in the equation $4x^2=-4x+16$ ?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find coefficient A

00:03 Arrange the equation so one side equals 0

00:20 Use the quadratic equation formula

00:26 We can see that coefficient A is for the X² term

00:31 Compare the formula to our equation to find coefficient A

00:34 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

What is the value of $a$ in the equation $4x^2=-4x+16$ ?

Step-by-step solution

To solve the problem, we need to express the given equation $4x^2 = -4x + 16$ in the standard quadratic form $ax^2 + bx + c = 0$ .

Let's perform the necessary transformations:
Rearrange the equation:

Start with: $4x^2 = -4x + 16$ .
Move all terms to one side to set the equation to zero:
$4x^2 + 4x - 16 = 0$ .

We now have the standard quadratic form:
$ax^2 + bx + c = 0$

In the equation $4x^2 + 4x - 16 = 0$ , the coefficient of $x^2$ is 4.

Thus, the value of $a$ is $\boxed{4}$ .

Final Answer

$a=4$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Rearrange to $ax^2 + bx + c = 0$ format
Technique: Move all terms to left side: $4x^2 + 4x - 16 = 0$
Check: Coefficient of $x^2$ term gives a-value: 4 ✓

Common Mistakes

Avoid these frequent errors

Identifying coefficient from wrong form of equation
Don't read the coefficient directly from $4x^2 = -4x + 16$ = missing the standard form requirement! This skips the essential rearrangement step. Always rearrange to $ax^2 + bx + c = 0$ first, then identify coefficients.

Practice Quiz

Test your knowledge with interactive questions

a = Coefficient of x²

b = Coefficient of x

c = Coefficient of the independent number

what is the value of $$ a $$ in the equation

$$ y=3x-10+5x^2 $$

FAQ

Everything you need to know about this question

Why do I need to rearrange to standard form first?

The standard form $ax^2 + bx + c = 0$ is the universal format for identifying coefficients. Without rearranging, you might miss terms or get confused about signs!

What if the equation is already equal to zero?

Lucky you! If it's already in the form $ax^2 + bx + c = 0$ , you can immediately identify the coefficients without rearranging.

How do I handle the negative signs when rearranging?

When moving terms across the equals sign, flip their signs. So $-4x$ becomes $+4x$ and $+16$ becomes $-16$ .

What are the b and c values in this equation?

From $4x^2 + 4x - 16 = 0$ : b = 4 (coefficient of x) and c = -16 (constant term). Remember to include the signs!

Can I divide the whole equation by a number first?

Yes! You can divide by any non-zero number to simplify, but the question asks for the original coefficient. So identify a before simplifying.

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