Use Quadratic Formula:** \( x = \frac{-70 \pm \sqrt{70^2 - 4 \times 4 \times (-150)}}{2 \times 4} \)

["# Use the Quadratic Formula: Solve Any Quadratic Equation Easyly", "Solving quadratic equations is a fundamental skill in algebra, essential for students, educators, and professionals in STEM fields. One of the most powerful tools for finding the roots of any quadratic equation is the Quadratic Formula. Whether you're tackling homework, preparing for exams, or working on real-world problems, knowing how to apply this formula can save valuable time and reduce errors.", "## What is the Quadratic Formula?", "The quadratic formula helps solve equations of the form:", "[\nax^2 + bx + c = 0\n]", "where ( a ), ( b ), and ( c ) are constants and ( a <br/>\neq 0 ). The formula is:", "[\nx = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\n]", "This solution works regardless of whether the equation has real or imaginary roots—provided you correctly compute the discriminant ( D = b^2 - 4ac ).", "## Step-by-Step Example: Use Quadratic Formula for ( x = \frac{-70 \pm \sqrt{70^2 - 4 \ imes 4 \ imes (-150)}}{2 \ imes 4} )", "Let’s apply the quadratic formula to the equation:", "[\nx = \frac{-70 \pm \sqrt{70^2 - 4 \ imes 4 \ imes (-150)}}{2 \ imes 4}\n]", "### Step 1: Identify coefficients\nFrom the equation ( x = -70 \pm \sqrt{\ldots} ), we conclude:\n- ( a = 4 )\n- ( b = -70 )\n- ( c = -150 )", "### Step 2: Plug into the formula\nSubstitute the values into the quadratic formula:", "[\nx = \frac{-(-70) \pm \sqrt{(-70)^2 - 4 \ imes 4 \ imes (-150)}}{2 \ imes 4}\n]", "Simplify the expression:", "[\nx = \frac{70 \pm \sqrt{4900 + 2400}}{8}\n]", "[\nx = \frac{70 \pm \sqrt{7300}}{8}\n]", "### Step 3: Simplify the square root\n[\n\sqrt{7300} = \sqrt{100 \ imes 73} = 10\sqrt{73}\n]", "So the solution becomes:", "[\nx = \frac{70 \pm 10\sqrt{73}}{8}\n]", "### Step 4: Reduce the fraction\nDivide both numerator terms by 2:", "[\nx = \frac{35 \pm 5\sqrt{73}}{4}\n]", "---", "## Why This Matters: Benefits of Using the Quadratic Formula", "- Universality: Always produces accurate roots for any quadratic equation.\n- Efficiency: Eliminates trial-and-error methods like factoring, especially for complex coefficients.\n- Insight: The discriminant reveals critical information:\n - If ( D > 0 ): Two distinct real roots.\n - If ( D = 0 ): One real root (a repeated root).\n - If ( D < 0 ): Two complex conjugate roots.", "---", "## Real-World Applications", "The quadratic formula is not just academic—it applies in physics (projectile motion), engineering (structural design), economics (profit-maximizing solutions), and more. Being able to quickly apply this formula empowers faster, confident problem-solving.", "## Final Thoughts", "Using the quadratic formula ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ) is a reliable and efficient way to solve quadratic equations. For the specific case of ( x = \frac{-70 \pm \sqrt{70^2 - 4 \ imes 4 \ imes (-150)}}{2 \ imes 4} ), the process demonstrates precision and clarity—key traits for mastering algebra.", "Start practicing this formula today, and watch your confidence grow in solving quadratic equations effortlessly!"]