Solve 0=0.16(h-8)^2

$$0 = 0.16 ( h - 8 ) ^ { 2 }$$

Solve for h

$$h=8$$

Steps Using Factoring

Divide both sides by 0.16. Zero divided by any non-zero number gives zero.

$$0=\left(h-8\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(h-8\right)^{2}.

$$0=h^{2}-16h+64$$

Swap sides so that all variable terms are on the left hand side.

$$h^{2}-16h+64=0$$

To solve the equation, factor h^{2}-16h+64 using formula h^{2}+\left(a+b\right)h+ab=\left(h+a\right)\left(h+b\right). To find a and b, set up a system to be solved.

$$a+b=-16 ab=64$$

Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. List all such integer pairs that give product 64.

$$-1,-64 -2,-32 -4,-16 -8,-8$$

Calculate the sum for each pair.

$$-1-64=-65 -2-32=-34 -4-16=-20 -8-8=-16$$

The solution is the pair that gives sum -16.

$$a=-8 b=-8$$

Rewrite factored expression \left(h+a\right)\left(h+b\right) using the obtained values.

$$\left(h-8\right)\left(h-8\right)$$

Rewrite as a binomial square.

$$\left(h-8\right)^{2}$$

To find equation solution, solve h-8=0.

$$h=8$$

Steps Using Factoring By Grouping

Divide both sides by 0.16. Zero divided by any non-zero number gives zero.

$$0=\left(h-8\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(h-8\right)^{2}.

$$0=h^{2}-16h+64$$

Swap sides so that all variable terms are on the left hand side.

$$h^{2}-16h+64=0$$

To solve the equation, factor the left hand side by grouping. First, left hand side needs to be rewritten as h^{2}+ah+bh+64. To find a and b, set up a system to be solved.

$$a+b=-16 ab=1\times 64=64$$

Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. List all such integer pairs that give product 64.

$$-1,-64 -2,-32 -4,-16 -8,-8$$

Calculate the sum for each pair.

$$-1-64=-65 -2-32=-34 -4-16=-20 -8-8=-16$$

The solution is the pair that gives sum -16.

$$a=-8 b=-8$$

Rewrite h^{2}-16h+64 as \left(h^{2}-8h\right)+\left(-8h+64\right).

$$\left(h^{2}-8h\right)+\left(-8h+64\right)$$

Factor out h in the first and -8 in the second group.

$$h\left(h-8\right)-8\left(h-8\right)$$

Factor out common term h-8 by using distributive property.

$$\left(h-8\right)\left(h-8\right)$$

Rewrite as a binomial square.

$$\left(h-8\right)^{2}$$

To find equation solution, solve h-8=0.

$$h=8$$

Steps Using the Quadratic Formula

Divide both sides by 0.16. Zero divided by any non-zero number gives zero.

$$0=\left(h-8\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(h-8\right)^{2}.

$$0=h^{2}-16h+64$$

Swap sides so that all variable terms are on the left hand side.

$$h^{2}-16h+64=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -16 for b, and 64 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$h=\frac{-\left(-16\right)±\sqrt{\left(-16\right)^{2}-4\times 64}}{2}$$

Square -16.

$$h=\frac{-\left(-16\right)±\sqrt{256-4\times 64}}{2}$$

Multiply -4 times 64.

$$h=\frac{-\left(-16\right)±\sqrt{256-256}}{2}$$

Add 256 to -256.

$$h=\frac{-\left(-16\right)±\sqrt{0}}{2}$$

Take the square root of 0.

$$h=-\frac{-16}{2}$$

The opposite of -16 is 16.

$$h=\frac{16}{2}$$

Divide 16 by 2.

$$h=8$$

Steps for Completing the Square

Divide both sides by 0.16. Zero divided by any non-zero number gives zero.

$$0=\left(h-8\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(h-8\right)^{2}.

$$0=h^{2}-16h+64$$

Swap sides so that all variable terms are on the left hand side.

$$h^{2}-16h+64=0$$

Factor h^{2}-16h+64. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(h-8\right)^{2}=0$$

Take the square root of both sides of the equation.

$$\sqrt{\left(h-8\right)^{2}}=\sqrt{0}$$

Simplify.

$$h-8=0 h-8=0$$

Add 8 to both sides of the equation.

$$h=8 h=8$$

The equation is now solved. Solutions are the same.

$$h=8$$