Follow the process of completing the square to solve x2 = -4x + 3

x1 = 0.64575

x2 = -4.64574

Step-by-step explanation:

Step 1: We want to rearrange the equation so all the variables are on one side

0 = -x² - 4x + 3

Step 2: We take out -1 in the first 2 terms so a = 1

0 = -(x² + 4x) + 3

Step 3: Force a square, take the 'b' value and divide it by 2 and square the result. Add it and subtract it from the inside of the brackets

b = 4

4/2 = 2

2² = 4

0 = -(x² + 4x + 4 - 4) + 3

Step 4: Move the -4 out remembering to apply the -

= -(x² + 4x + 4) + 4 + 3

Step 5: We notice is inside the brackets is a perfect square

0 = -(x + 2)² + 7

Therefore the vertex form of the equation is

y = -(x + 2)² + 7

Step 6: We want to solve the equation (find the x intercepts) so we set y to 0 and solve for x

0 = -(x + 2)² + 7

-7 = -(x + 2)²

7 = (x + 2)²

1st Solution:

x = +2.64575 - 2

x = 0.64575

2nd Solution:

x = -2.64575 - 2

x = -4.64574

step-by-step explanation:

here's what happens:

1) the graph of f   = x^2 is shifted 2 units to the right.

2) the resulting graph is reflected in the x-axis, so that the parabola now opens down.

3) this final result is transformed up by 5 units.