Combine like terms: \(4x^2 + 50x + 150 = 286\).

["Title: Combine Like Terms and Solve the Equation: A Step-by-Step Guide", "When solving quadratic equations, one of the first essential skills is combining like terms. This process simplifies expressions by gathering identical terms together—critical for solving equations effectively. In this article, we explore how to combine like terms and apply them to solve the equation:\n[\n4x^2 + 50x + 150 = 286\n]", "---", "### What Are Like Terms?", "Like terms are those that contain the same variables raised to the same powers. In polynomials, constant terms (numbers with no variables) are also considered like terms when grouped together.", "For example, in the expression (4x^2 + 50x + 150), the terms have different powers of (x), so they are not like terms and cannot be combined directly.", "However, combining like terms is key before simplifying complex equations or isolating variables.", "---", "### Step 1: Rewrite the Equation by Combining Constants", "The given equation is:\n[\n4x^2 + 50x + 150 = 286\n]", "To simplify, subtract 286 from both sides to move all terms to one side and form a standard quadratic equation:\n[\n4x^2 + 50x + 150 - 286 = 0\n]", "Now simplify the constants:\n[\n4x^2 + 50x - 136 = 0\n]", "Although we cannot combine the constants (150) and (-286) into a single term here—since they are unlike constants—it’s important to recognize that any algebraic expression with like terms subtracted must be simplified completely before proceeding to isolate (x).", "---", "### Step 2: Use Combining Like Terms to Simplify If Possible", "In this equation, the terms are:\n- (4x^2) (quadratic term)\n- (50x) (linear term)\n- (-136) (constant)", "There are no like terms to combine beyond confirming that each term is distinct in variable content or degree. This is crucial because combining terms incorrectly can lead to algebraic errors.", "Thus, the simplified standard form is:\n[\n4x^2 + 50x - 136 = 0\n]", "---", "### Step 3: Solve the Simplified Quadratic Equation", "Now solve:\n[\n4x^2 + 50x - 136 = 0\n]", "Divide the entire equation by 2 to simplify calculations:\n[\n2x^2 + 25x - 68 = 0\n]", "This form maintains integer coefficients and is easier to factor or apply the quadratic formula.", "---", "### Step 4: Apply the Quadratic Formula", "Use the quadratic formula:\n[\nx = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\n]", "Here, (a = 2), (b = 25), (c = -68).", "Calculate the discriminant:\n[\nb^2 - 4ac = 25^2 - 4(2)(-68) = 625 + 544 = 1169\n]", "Since 1169 is not a perfect square, we keep the solution in radical form:\n[\nx = \frac{-25 \pm \sqrt{1169}}{4}\n]", "---", "### Final Answer", "The solutions to the equation (4x^2 + 50x + 150 = 286) are:\n[\nx = \frac{-25 + \sqrt{1169}}{4} \quad \ ext{and} \quad x = \frac{-25 - \sqrt{1169}}{4}\n]", "---", "### Key Takeaways", "- Combining like terms streamlines expressions, essential before solving equations.\n- In original form, constants (150 + 50x + 136) cannot be merged—analyze similarities carefully.\n- Standard form (ax^2 + bx + c = 0) allows direct application of solving techniques like factoring, completing the square, or the quadratic formula.\n- Simplifying coefficients (e.g., dividing by common factors) reduces computational complexity.", "Mastering the combination of like terms unlocks stronger algebraic problem-solving skills—critical for everyone from students to professionals working with mathematical models.", "---", "Keywords: combine like terms, solve (4x^2 + 50x + 150 = 286), quadratic equation, quadratic formula, algebra tutorial, simplify equations, standard form quadratic", "Meta Description: Learn how to combine like terms and solve (4x^2 + 50x + 150 = 286) step-by-step. Master algebraic simplification and error-free equation solving."]