Solve the quadratic equation ax2+bx+c=0 using the completing the squares
step 1) 1/(ax^2+bx+c)=0*1/a
x^2+b/a(x)=-c/a
x^2+b/a(x)=-c/a
step2) add {1/2*b/a}^2=b^2/4a to both sides:x^2+b/a(x)+b^2/4a=b^2/4a-c/a=b^2-4ac/4a^2
step3) x^2+b/a(x)+b^2/4a write as {x+b/a}^2=b^2-4ac/4a^2
x=-b+or- *square root of b^2-4ac/2a. you get the general formula.
kahit ano
To solve a quadratic equation using the method of completing the square, follow these steps:
Step 1: Make sure the quadratic equation is in the standard form: ax^2 + bx + c = 0, where a, b, and c are constants.
Step 2: Divide the entire equation by a (if needed), so the coefficient of x^2 is 1.
Step 3: Move the constant term (c) to the right side of the equation, keeping the x^2 and x terms on the left side.
Step 4: Take half of the coefficient of x (b/2) and square it [(b/2)^2]. This new value will be used for completing the square.
Step 5: Add the squared value from step 4 to both sides of the equation to make a perfect square trinomial on the left side.
Step 6: Factor the perfect square trinomial on the left side into a binomial. This is done by taking the square root of the squared value from step 4 and placing it as the middle term of the binomial.
Step 7: Rewrite the equation with the square of the binomial factored in step 6.
Step 8: Take the square root of both sides of the equation.
Step 9: Solve the equation for x by isolating x on one side of the equation.
Step 10: Write the solution as x = [value(s)].
Now, let's solve the quadratic equation ax^2 + bx + c = 0 using the completing the square method:
Example: Solve the equation 2x^2 + 4x - 6 = 0
Step 1: The equation is already in standard form.
Step 2: No division is required.
Step 3: Move the constant term to the right side: 2x^2 + 4x = 6.
Step 4: Take half of the coefficient of x: (4/2)^2 = 4.
Step 5: Add 4 to both sides: 2x^2 + 4x + 4 = 6 + 4.
Step 6: Factor the perfect square trinomial: (x + 2)^2 = 10.
Step 7: Rewrite the equation: (x + 2)^2 = 10.
Step 8: Take the square root of both sides: √((x + 2)^2) = √10.
Step 9: Solve for x: x + 2 = ±√10.
Step 10: Write the solution: x = -2 ± √10.
Therefore, the solutions to the quadratic equation 2x^2 + 4x - 6 = 0 using the completing the square method are x = -2 + √10 and x = -2 - √10.