Expanding: \( 600 + 60x + 40x + 4x^2 = 1,056 \)

["Expanding the Equation: Solve ( 600 + 60x + 40x + 4x^2 = 1,056 ) Step-by-Step", "When solving quadratic equations, proper expansion and simplification are key to finding accurate solutions. In this article, we walk through expanding and solving the equation:", "[ 600 + 60x + 40x + 4x^2 = 1,056 ]", "---", "### Step 1: Simplify the Left-Hand Side", "Start by combining like terms on the left-hand side. Combine the linear terms (60x) and (40x):", "[ 600 + 60x + 40x + 4x^2 = 600 + 100x + 4x^2 ]", "So the equation becomes:", "[ 4x^2 + 100x + 600 = 1,056 ]", "---", "### Step 2: Move All Terms to One Side", "To set the equation to zero (standard quadratic form), subtract 1,056 from both sides:", "[ 4x^2 + 100x + 600 - 1,056 = 0 ]", "[ 4x^2 + 100x - 456 = 0 ]", "---", "### Step 3: Simplify the Quadratic Equation (Optional but Helpful)", "Check if the equation can be simplified. All coefficients are divisible by 4:", "[ \frac{4x^2 + 100x - 456}{4} = 0 ]", "[ x^2 + 25x - 114 = 0 ]", "Now we have the simplified quadratic:", "[ x^2 + 25x - 114 = 0 ]", "---", "### Step 4: Solve Using the Quadratic Formula", "For ( ax^2 + bx + c = 0 ), the solutions are:", "[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]", "Here, ( a = 1 ), ( b = 25 ), ( c = -114 ):", "[ x = \frac{-25 \pm \sqrt{25^2 - 4(1)(-114)}}{2(1)} ]", "[ x = \frac{-25 \pm \sqrt{625 + 456}}{2} ]", "[ x = \frac{-25 \pm \sqrt{1,081}}{2} ]", "Note: ( \sqrt{1,081} = 32.9 ) approximately, but check if 1,081 is a perfect square.", "Indeed, ( 32^2 = 1,024 ), ( 33^2 = 1,089 ), so ( 1,081 ) is not a perfect square, but we can leave the answer in exact form.", "---", "### Final Solutions:\n[ x = \frac{-25 \pm \sqrt{1,081}}{2} ]", "---", "### Summary", "- Combined like terms carefully.\n- Moved all terms to one side to form a standard quadratic equation.\n- Simplified by dividing through by the GCD (4).\n- Applied the quadratic formula to find solutions.", "This structured approach ensures clarity and accuracy—critical when expanding and solving equations like ( 600 + 60x + 40x + 4x^2 = 1,056 ).", "---", "Keywords for SEO:\nExpanding quadratic equation, solve ( 4x^2 + 100x + 600 = 1,056 ), simplify quadratic equation, quadratic formula step-by-step, solving 600 + 60x + 40x + 4x² = 1056, step-by-step equation expansion, algebraic simplification, quadratic solution method, linear and quadratic combination, precise equation solving.", "---", "Check your solution by substituting back into the original equation to confirm correctness. Mastering expansion and simplification opens the door to solving more complex equations efficiently."]