The quadratic equation ax²+bx+c = 0 is given and this is illustrated below.
<h3>How to illustrate the equation?</h3>
ax²+bx+c = 0
Step 1: Subtract c from both sides
ax²+bx+c-c = 0-c
ax²+bx = -c
Step 2: Divide both sides of the equation by a
ax²/a + bx/a = -c/a
x² + bx/a = -c/a
Step 3: Complete the square and add the quantity (b/2a)² times a squared to both sides
x² + bx/a + (b/2a)² = -c/a + (b/2a)²
Step 4: Square the quantity b/2a on the right side of the equation
x² + bx/a + (b/2a)² = -c/a + b²/4a²
Step 5: Find a common denominator on the right side of the equation which is 4a²
x² + bx/a + (b/2a)² = -4ac/4a² + b²/4a²
Step 6: Add the fractions together on the right side of the equation
x² + bx/a + (b/2a)² = (-4ac+ b²)/4a²
Step 7: The equation on the left is to be written as a perfect square as shown
(x+b/2a)² = (-4ac+ b²)/4a²
Step 8: Take the square root of both sides
√(x+b/2a)² = √ (-4ac+ b²)/4a²
(x+b/2a) = √(-4ac+ b²)/2a
Step 9: subtract b/2a from both sides
x+b/2a - b/2a = -b/2a + √(-4ac+ b²)/2a
x = -b/2a + √(-4ac+ b²)/2a
Step 10: Add the fractions together on the right-hand side
x = -b±√(-4ac+ b²)/2a
This will then gives the required equation.
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