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The Square Root Principle & Completing the Square Consider To x2 = 25. What is x? solve equations of the form ax2 + c = d: Isolate the squared term Apply a square root to each side of the equation. Remember, it can be positive or negative! 1. 2. 3. 4. 5. k2 + 5 = 30 - 2 m2 = - 27 3 32 4n2 + 20 = -76 (6h – 5)2 = 81 (3x – 4)2 + 1 = -80 To solve ax2 + bx + c = 0 1. Divide everything by a to make the leading coefficient 1 2. Isolate the variable terms on one side. 3. Take half the coefficient of the linear term and Square it. Add that value to both sides. 4. Rewrite the left side as a binomial squared. 5. Solve. 1. c2 – 6c + 45 = 0 2. a2 = 6a – 8 3. 4x2 = 24x + 11 4. 2x2 - 5x – 12 = 0