Subtract 936 from both sides: \( 4x^2 + 100x - 336 = 0 \).

["# Simplifying the Quadratic Equation: Subtracting 936 from Both Sides", "When solving quadratic equations, simplifying the equation by eliminating constants from both sides can make the process more manageable. In this article, we’ll explore how subtracting 936 from both sides of the equation:", "[\n4x^2 + 100x - 336 = 0\n]\ncan help streamline solving the equation ( 4x^2 + 100x - 336 = 0 ).", "## Why Subtract 936 From Both Sides?", "The original equation:\n[\n4x^2 + 100x - 336 = 0\n]\ncontains the constant term (-336). However, in some problem contexts—such as when preparing equations for factoring, completing the square, or graphing—removing constants can simplify manipulation and reveal hidden structure.", "Although 936 isn’t part of the original constant term in degree, subtracting 936 from both sides creates a balanced transformation:", "[\n4x^2 + 100x - 336 - 936 = 0 - 936\n]\n[\n4x^2 + 100x - 1272 = 0\n]", "This step doesn't change the equation’s solution set—it only reshapes the expression for clarity or convenience.", "## Step-by-Step Simplification", "Start with the original quadratic equation:\n[\n4x^2 + 100x - 336 = 0\n]", "### Step 1: Subtract 936 from both sides\n[\n4x^2 + 100x - 336 - 936 = 0 - 936\n]\n[\n4x^2 + 100x - 1272 = 0\n]", "### Step 2: Simplify the constant coefficient", "Factor out the greatest common divisor (GCD) of the coefficients:\nThe coefficients are 4, 100, and 1272. The GCD is 4:", "[\n4(x^2 + 25x - 318) = 0\n]", "### Step 3: Divide both sides by 4", "To simplify, divide each term by 4:\n[\nx^2 + 25x - 318 = 0\n]", "---", "## Result: A Cleaner Form for Solving", "The equation is now:\n[\nx^2 + 25x - 318 = 0\n]", "This form is often easier to work with for factoring attempts, completing the square, or applying the quadratic formula.", "---", "## Solving the Simplified Equation", "### Using the Quadratic Formula", "The quadratic formula is:\n[\nx = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\n]", "For ( x^2 + 25x - 318 = 0 ):\n- ( a = 1 )\n- ( b = 25 )\n- ( c = -318 )", "Calculate the discriminant:\n[\n\Delta = b^2 - 4ac = 25^2 - 4(1)(-318) = 625 + 1272 = 1897\n]", "Now apply the formula:\n[\nx = \frac{-25 \pm \sqrt{1897}}{2}\n]", "Since ( \sqrt{1897} ) is irrational, leave the solution in exact form:\n[\nx = \frac{-25 \pm \sqrt{1897}}{2}\n]", "### Alternatively: Factoring (if possible)", "Check if ( x^2 + 25x - 318 ) factors nicely. We seek two numbers that multiply to (-318) and add to (25).", "Factors of 318:\n- (1, 2, 3, 6, 53, 106, 159, 318)", "Testing pairs, we find:\n[\n318 = 53 \cdot (-6) \quad \ ext{since} \quad 53 + (-6) = 47 \quad \ ext{(too low)}\n]\nTry:\n[\n159 \cdot (-2) = -318, \quad 159 - 2 = 157\n]\nNo integer pair sums to 25. So factoring is impractical—sticking with the quadratic formula is best.", "---", "## Summary", "Subtracting 936 from both sides of ( 4x^2 + 100x - 336 = 0 ) led to:\n[\n4x^2 + 100x - 1272 = 0 \quad \Rightarrow \quad x^2 + 25x - 318 = 0\n]", "This reduced equation simplifies-solving and maintains the original equation’s solutions. Using the quadratic formula, the solutions are:", "[\n\boxed{x = \frac{-25 \pm \sqrt{1897}}{2}}\n]", "This method exemplifies how small algebraic manipulations—like subtracting constants—helping streamline solving quadratic equations efficiently.", "---", "Keywords:\nquadratic equation solver, subtract 936 from both sides, simplify (4x^2 + 100x - 336 = 0), quadratic formula, completing the square, simplify algebra, equation solving tips", "Meta Description:\nLearn how subtracting 936 from both sides of (4x^2 + 100x - 336 = 0) simplifies the equation, leads to a cleaner form (x^2 + 25x - 318 = 0), and enables efficient use of the quadratic formula."]