["# Solving the Equation: ( x^2 + x^2 + 4x + 4 = 340 ) – A Step-by-Step Guide", "If you're looking to solve the quadratic equation ( x^2 + x^2 + 4x + 4 = 340 ), you're not alone — this type of algebraic expression appears frequently in math homework, classroom problems, and real-world applications. In this comprehensive SEO-optimized article, we’ll walk you through simplifying, solving, and interpreting this equation, while also sharing key insights and techniques to master quadratic equations.", "---", "## Understanding the Equation: ( x^2 + x^2 + 4x + 4 = 340 )", "The given equation starts with two identical ( x^2 ) terms, which can be easily combined:", "[
\nx^2 + x^2 + 4x + 4 = 340
\n]", "Simplify:", "[
\n2x^2 + 4x + 4 = 340
\n]", "Now, subtract 340 from both sides to bring the equation to standard quadratic form:", "[
\n2x^2 + 4x + 4 - 340 = 0
\n]
\n[
\n2x^2 + 4x - 336 = 0
\n]", "This is a standard quadratic equation of the form ( ax^2 + bx + c = 0 ), where:
\n- ( a = 2 )
\n- ( b = 4 )
\n- ( c = -336 )", "---", "## Step-by-Step Solution: How to Solve ( 2x^2 + 4x - 336 = 0 )", "### Step 1: Simplify by Dividing by the Greatest Common Factor (GCF)
\nSince all coefficients share a common factor of 2, divide the entire equation by 2:", "[
\nx^2 + 2x - 168 = 0
\n]", "This makes solving easier without changing the roots.", "### Step 2: Apply the Quadratic Formula
\nThe quadratic formula is:", "[
\nx = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\n]", "Substitute ( a = 1 ), ( b = 2 ), ( c = -168 ):", "[
\nx = \frac{-2 \pm \sqrt{(2)^2 - 4(1)(-168)}}{2(1)}
\n]
\n[
\nx = \frac{-2 \pm \sqrt{4 + 672}}{2}
\n]
\n[
\nx = \frac{-2 \pm \sqrt{676}}{2}
\n]
\n[
\nx = \frac{-2 \pm 26}{2}
\n]", "### Step 3: Calculate the Two Solutions", "[
\nx = \frac{-2 + 26}{2} = \frac{24}{2} = 12
\n]
\n[
\nx = \frac{-2 - 26}{2} = \frac{-28}{2} = -14
\n]", "---", "## Final Solutions", "The solutions to the equation ( x^2 + x^2 + 4x + 4 = 340 ) are:", "[
\n\boxed{x = 12 \quad} \ ext{and} \quad x = -14
\n]", "---", "## Why Understanding This Equation Matters", "Solving equations like ( x^2 + x^2 + 4x + 4 = 340 ) is not only critical in algebra but also foundational for studying real-world problems such as projectile motion, optimization, economics, and physics simulations.", "---", "## Tips for Solving Similar Quadratic Equations", "- Always simplify before applying formulas.
\n- Group like terms carefully.
\n- Use the quadratic formula when factoring is difficult or impossible.
\n- Always verify solutions by plugging them back into the original equation.", "---", "## Related SEO Keywords", "- How to solve ( x^2 + x^2 + 4x + 4 = 340 )
\n- Step-by-step quadratic equation solver
\n- Learn quadratic formulas and graphing
\n- Simplify and solve ( 2x^2 + 4x - 336 = 0 )
\n- Solve quadratic equations with real-world context", "---", "## Conclusion", "Solving ( x^2 + x^2 + 4x + 4 = 340 ) involves simplifying the expression, forming a standard quadratic equation, and applying the quadratic formula — a powerful tool for anyone studying algebra. Mastering these techniques equips you with a strong foundation for tackling more complex mathematical challenges.", "If you're looking to deepen your algebra skills or solve similar problems with confidence, practice is key! Use this article as a reference, and always double-check your work.", "---", "Meta Description:
\nLearn how to solve ( x^2 + x^2 + 4x + 4 = 340 ) step-by-step. Understand simplification, apply the quadratic formula, and verify solutions for accurate results. Ideal for math students and educators.", "Keywords: ( x^2 + x^2 + 4x + 4 = 340 ), quadratic equation, solve quadratics, simplify equations, quadratic formula, algebra tips, math homework help."]
