Question

(4х+1)^2-(4х-3)(4х+3)=42

Answer 1

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Answer 2

Let's solve the equation step by step:

Step 1: Expand the expressions on both sides of the equation.

To expand the left side of the equation, we'll use the formula for squaring a binomial: (a + b)^2 = a^2 + 2ab + b^2.

Expanding the left side: (4x + 1)^2 - (4x - 3)(4x + 3) = (4x)^2 + 2(4x)(1) + 1^2 - (16x^2 - 3^2)

Simplifying further: = 16x^2 + 8x + 1 - (16x^2 - 9)

Step 2: Continue simplifying the equation.

Now, let's combine like terms and distribute the negative sign in front of the second term: = 16x^2 + 8x + 1 - 16x^2 + 9

Step 3: Further simplify the equation.

Notice that the 16x^2 terms will cancel out, leaving only the constant terms: = 8x + 1 + 9

Step 4: Combine the constant terms: = 8x + 10

Now, the equation becomes: 8x + 10 = 42

Step 5: Isolate the variable on one side of the equation.

To isolate x, we need to move the constant term to the other side of the equation. Since the constant term is positive, we'll subtract 10 from both sides: 8x = 42 - 10 8x = 32

Step 6: Solve for x.

Finally, to find the value of x, divide both sides by 8: x = 32 / 8 x = 4

So, the solution to the equation is x = 4. You can verify this by substituting x with 4 in the original equation to see if it holds true.