Subtract 145: \( 2x^2 + 2x - 144 = 0 \) → divide by 2: \( x^2 + x - 72 = 0 \)

["Title: How to Solve ( 2x^2 + 2x - 144 = 0 ): A Step-by-Step Guide Dividing by 2", "Meta Description:\nLearn how to simplify and solve the quadratic equation ( 2x^2 + 2x - 144 = 0 ) efficiently by dividing every term by 2 to get ( x^2 + x - 72 = 0 ). Discover factoring, solving methods, and practical tips for quick quadratic results.", "---", "### Introduction\nQuadratic equations—expressions like ( ax^2 + bx + c = 0 )—are fundamental in algebra, but solving them can sometimes feel overwhelming. A common challenge students face is dealing with leading coefficients not equal to 1, which complicates factoring and applications.", "One practical strategy is simplifying the equation by dividing every term by the leading coefficient. In this article, we'll explore solving the equation:\n[ 2x^2 + 2x - 144 = 0 ]\nby dividing through by 2 to make it easier:\n[ x^2 + x - 72 = 0 ]\nThis transformation enables clearer factoring and faster solutions. Ready to dive in?", "---", "### Simplifying the Equation: Divide by 2", "Starting with the original quadratic:\n[\n2x^2 + 2x - 144 = 0\n]\nDivide every term by 2:\n[\n\frac{2x^2}{2} + \frac{2x}{2} - \frac{144}{2} = 0\n]\nSimplifies directly to:\n[\nx^2 + x - 72 = 0\n]", "Why simplify?\n- The new equation has a cleaner, simpler form.\n- It’s easier to factor or apply the quadratic formula.\n- You reduce the chance of arithmetic errors during calculations.", "---", "### Solving the Simplified Equation: Step-by-Step", "Now solving:\n[\nx^2 + x - 72 = 0\n]", "Step 1: Factoring Approach (Recommended for Simple Discriminants)\nWe look for two numbers that multiply to ( -72 ) and add to ( 1 ) (the coefficient of ( x )).", "Try factor pairs of ( -72 ):\n- ( 9 ) and ( -8 ): ( 9 \ imes (-8) = -72 ), ( 9 + (-8) = 1 ) → Perfect!", "So we write:\n[\n(x + 9)(x - 8) = 0\n]", "Set each factor equal to zero:\n[\nx + 9 = 0 \quad \Rightarrow \quad x = -9\n]\n[\nx - 8 = 0 \quad \Rightarrow \quad x = 8\n]", "Solutions:\n[\nx = -9 \quad \ ext{and} \quad x = 8\n]", "Step 2: Verifying with the Quadratic Formula\nFor confirmation, use the standard quadratic formula:\n[\nx = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\n]\nFor ( x^2 + x - 72 = 0 ), ( a = 1 ), ( b = 1 ), ( c = -72 ).", "Calculate discriminant:\n[\n\Delta = b^2 - 4ac = 1^2 - 4(1)(-72) = 1 + 288 = 289\n]", "Take square root:\n[\n\sqrt{289} = 17\n]", "Now find solutions:\n[\nx = \frac{-1 \pm 17}{2}\n]\n- ( x = \frac{-1 + 17}{2} = \frac{16}{2} = 8 )\n- ( x = \frac{-1 - 17}{2} = \frac{-18}{2} = -9 )", "Matches our earlier result!", "---", "### Why This Simplification Matters", "Dividing by the leading coefficient early makes solving quadratics more intuitive:\n- Reduces computational complexity.\n- Helps uncover patterns like factorable forms.\n- Minimizes error when applying formulas.", "If the original equation had been harder to factor (e.g., larger constants or no obvious integer pairs), dividing by 2 would still be a smart preprocessing step.", "---", "### Summary", "To solve ( 2x^2 + 2x - 144 = 0 ):\n1. Divide all terms by 2 to get ( x^2 + x - 72 = 0 ).\n2. Factor using numbers multiplying to ( -72 ) and adding to ( 1 ): ( (x + 9)(x - 8) = 0 ).\n3. Solve set each factor to zero: ( x = -9 ) and ( x = 8 ).\n4. Confirm using the quadratic formula yields the same solutions.", "Mastering equation simplification like dividing by the leading coefficient is key to efficient algebra. Practice turns these steps into quick reflexes—enjoy solving quadratic equations with confidence!", "---", "Keywords: quadratic equation, solve ( x^2 + x - 72 = 0 ), simplify quadratic equation, factoring quadratics, divide by 2, quadratic formula, algebraic methods, solving ( 2x^2 + 2x - 144 = 0 ), X² + X - 72 = 0 solutions", "Related Articles:\n- How to Factor ( x^2 + x - 72 ) Easily\n- Quadratic Formula vs. Factoring: Which Method to Use?\n- Quadratic Equations for Beginners: Step-by-Step Examples", "---", "Whether solving for homework, professional work, or just curiosity, simplifying quadratics is a valuable skill—start with dividing by the leading coefficient and watch your math skills grow!"]