Finding the Value of x in an Algebraic Equation

We are asked to find the value of $x$ that satisfies the given equation:

$5(5x^2 - 5) - 5(5x^2 + 7x - 2) = 14$

Step 1: Distribute the constants

First, distribute the number 5 into each set of parentheses:

• For the first term: $5 \times (5x^2 - 5) = (5 \times 5x^2) - (5 \times 5) = 25x^2 - 25$
• For the second term: $5 \times (5x^2 + 7x - 2) = (5 \times 5x^2) + (5 \times 7x) - (5 \times 2) = 25x^2 + 35x - 10$

Substitute these back into the original equation:

$(25x^2 - 25) - (25x^2 + 35x - 10) = 14$

Step 2: Simplify the equation by removing parentheses

When removing the second set of parentheses, remember to change the sign of each term inside because of the minus sign in front:

$25x^2 - 25 - 25x^2 - 35x + 10 = 14$

Step 3: Combine like terms

Now, group and combine similar terms:

• Combine the $x^2$ terms: $25x^2 - 25x^2 = 0x^2 = 0$
• Combine the constant terms: $-25 + 10 = -15$
• The $x$ term is $-35x$

The equation simplifies to:

$0 - 35x - 15 = 14$

$ -35x - 15 = 14$

Step 4: Isolate the term containing x

To isolate the term $-35x$, add 15 to both sides of the equation:

$ -35x - 15 + 15 = 14 + 15$

$ -35x = 29$

Step 5: Solve for x

Finally, divide both sides by -35 to find the value of $x$:

$ x = \frac{29}{-35}$

$ x = -\frac{29}{35}$

Therefore, the value of $x$ that satisfies the equation is $-29/35$.