## Solve By Completing the Square

Solve each equation by Completing the Square.

## Checking Your Answers

- Equation: x^2 + 5x + 6 = 0 Show answer | Show step-by-step Answer: x = -3, -2 Hide answer | Show step-by-step
- Equation: x^2 + 2x + 1 = 0 Show answer | Show step-by-step Answer: x = -1 Hide answer | Show step-by-step
- Equation: x^2 + 3x - 10 = 0 Show answer | Show step-by-step Answer: x = -5, 2 Hide answer | Show step-by-step
- Equation: m^2 - 4m - 21 = 0 Show answer | Show step-by-step Answer: m = -3, 7 Hide answer | Show step-by-step
- Equation: 3k^2 + 18k + 15 = 0 Show answer | Show step-by-step Answer: k = -5, -1 Hide answer | Show step-by-step
- Equation: 2n^2 - 22n + 60 = 0 Show answer | Show step-by-step Answer: n = 5, 6 Hide answer | Show step-by-step
- Equation: 4y^2 + 8y - 21 = 0 Show answer | Show step-by-step Answer: y = -3.5, 1.5 Hide answer | Show step-by-step
- Equation: 8y^2 + 10y - 3 = 0 Show answer | Show step-by-step Answer: y = -1.5, 0.25 Hide answer | Show step-by-step
- Equation: 50k^2 - 20k - 6 = 0 Show answer | Show step-by-step Answer: k = -0.2, 0.6 Hide answer | Show step-by-step
- Equation: 100x^2 - 100x + 9 = 0 Show answer | Show step-by-step Answer: x = 0.1, 0.9 Hide answer | Show step-by-step
- Equation: 10t^2 = t + 2 Show answer | Show step-by-step Answer: t = -0.4, 0.5 Hide answer | Show step-by-step
- Equation: 18m^2 + 6m + 6 = 6m^2 + 30m - 3 Show answer | Show step-by-step Answer: m = 0.5, 1.5 Hide answer | Show step-by-step
- Equation: p^2 - 0.75p + 0.125 = 0 Show answer | Show step-by-step Answer: p = 0.25, 0.5 Hide answer | Show step-by-step
- Equation: 2x^2 = x^2 + 1.75 - 3x Show answer | Show step-by-step Answer: x = -3.5, 0.5 Hide answer | Show step-by-step
- Equation: x^2 = 0.6x - 0.08 Show answer | Show step-by-step Answer: x = 0.2, 0.4 Hide answer | Show step-by-step
- Equation: 3y^2 - 2.55y - 1.0 = 0.5 Show answer | Show step-by-step Answer: y = -0.4, 1.25 Hide answer | Show step-by-step
- Equation: j^2 - 3.5j + 1.5 = 0 Show answer | Show step-by-step Answer: j = 0.5, 3 Hide answer | Show step-by-step
- Equation: c^2 + 3.75c - 1 = 0 Show answer | Show step-by-step Answer: c = -4, 0.25 Hide answer | Show step-by-step
- Equation: w^2 + 10.1w + 1 = 0 Show answer | Show step-by-step Answer: w = -10, -0.1 Hide answer | Show step-by-step
- Equation: x^2 -11.5x - 6 = 0 Show answer | Show step-by-step Answer: x = -0.5, 12 Hide answer | Show step-by-step

## Related Pages

Completing the Square Calculator Solves equations by completing the square whenever possible.

## COMPLETING THE SQUARE WORKSHEET

Write x 2 + 6x + 7 = 0 in the form (x + p) 2 = q.

Solve the following quadratic equation using square root :

Solve the following quadratic equation by completing the square :

Write the following quadratic equation in vertex form and graph it :

What is the maximum or minimum value of the graph of the equation ?

Isolate the variable expression.

Determine the constant needed to complete the square.

Comparing x 2 + bx and x 2 + 6x, we get

In (1), we have to add 9 to each side.

Write the left side of the equation as a perfect square.

Hence, the equation x 2 + 6x + 7 = 0 can be written as

Recognize that the quadratic equation is a perfect square trinomial.

Factor the perfect square trinomial.

Take the square root on each side of the equation.

Comparing x 2 + bx and x 2 - 8x, we get

(b/2) 2 = (-8/2) 2 = (-4) 2 = 16

In (1), we have to add 16 to each side.

Factor out the x 2 coefficient, -1.

= -1( x 2 - 2 ⋅ x ⋅ 1 + 1 2 - 1 2 - 3 )

Hence, the vertex form of the equation y = -x 2 - 2x + 3 is

The vertex of the parabola is (1, 4).

In the given equation y = -x 2 - 2x + 3, the sign of x 2 is negative.

So, its graph is a parabola that opens down.

The graph of the given quadratic equation has a maximum of y = 4 at x = 1.

Let x and y be the length and width of the garden respectively.

Alex wants the area to be 6000 m 2 .

Comparing x 2 + bx and x 2 - 170x, we get

(b/2) 2 = (-170/2) 2 = (-85) 2 = 7225

In (1), we have to add 7225 to each side.

x 2 - 170x + 7225 = -6000 + 7225

In each case, there is 340 m of fencing used.

Likewise, the area is 6000 m 2 .

Hence, Alex should make two sides of the garden 120 m long and the other two sides 50 m long.

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