Question

solve by completing the square.
h² + 4h = -3
write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.
h = or h =
save answer

Explanation:

Step1: Complete the square for \(h^2 + 4h\)

To complete the square for the quadratic expression \(h^2 + 4h\), we take half of the coefficient of \(h\), which is \(\frac{4}{2}=2\), and then square it: \(2^2 = 4\). We add and subtract this value on the left - hand side of the equation \(h^2+4h=-3\). But since we are dealing with an equation, we can add 4 to both sides to maintain the equality.
The equation becomes \(h^2 + 4h+4=-3 + 4\).

Step2: Rewrite the left - hand side as a perfect square

The left - hand side \(h^2 + 4h + 4\) can be written as \((h + 2)^2\) according to the perfect square formula \((a + b)^2=a^2+2ab + b^2\) (here \(a = h\) and \(b = 2\)). The right - hand side is \(1\), so we have the equation \((h + 2)^2=1\).

Step3: Solve for \(h\)

Take the square root of both sides of the equation \((h + 2)^2=1\). We get \(h + 2=\pm\sqrt{1}\). Since \(\sqrt{1}=1\), we have two cases:

• Case 1: \(h+2 = 1\). Subtract 2 from both sides: \(h=1 - 2=-1\).
• Case 2: \(h + 2=-1\). Subtract 2 from both sides: \(h=-1 - 2=-3\).

Answer:

\(h=-1\) or \(h = - 3\)