Hints for solving the problems

Hints for solving the problems - Apply 10.1

Solving by Factoring

Problem No. 2 - Solve x² + 13x = 0 by factoring.

To solve a quadratic problem by factoring, move all terms to one side of the equation with a zero (0) on the other side. Make the sure the quadratic equation is in standard form. (ax² + bx + c = 0) Factor the quadratic equation and set each factor equal to zero (0) and solve the linear equations.

x² + 13x = 0 x(x + 13) = 0

x = 0 and x + 13 = 0

x = 0 and x = -13 {-13, 0} the answers

Problem No. 8 - Solve x² + 8x + 7 = 0 by factoring.

x² + 8x + 7 = 0 (x + 7)(x + 1) = 0

x + 7 = 0 and x + 1 = 0

x = -7 and x = -1 {-7, -1} the answers

Problem No. 14 - Solve x² - 3x - 40 = 0 by factoring.

x² - 3x - 40 = 0 (x - 8)(x + 5) = 0

x - 8 = 0 and x + 5 = 0

x = 8 and x = -5 {-5, 8) the answers

Problem No. 20 - Solve x² + 7x = 44 by factoring.

Move the 44 to the left side of the equation and change the sign.

x² + 7x - 44 = 0 (x + 11)(x - 4) = 0

x + 11 = 0 and x - 4 = 0

x = -11 and x = 4 {-11, 4} the answers

Problem No. 26 - Solve x² = 5x + 66 by factoring

Move both terms on the right side of the equation to the left and put the equation in standard form.

x² - 5x - 66 = 0 (x - 11)(x + 6) = 0

x - 11 = 0 and x + 6 = 0

x = 11 and x = -6 {-6, 11} the answers

Solving by Square Roots

Problem No. 30 - Solve x² = 81 using the square root property.

Using the square root property, you take the square root of both sides of the equation. First you must have the variable isolated on one side of the equation and the constants on the other side.

x² = 81 x = ±9 the answers

Please remember when you take the square root of a variable or binomial with a variable squared you get the radicand, such as;

and . Also don’t forget that when you take the square root of a term there are two answers. Remember the square root of 49 will have two answers. (±7). Put the ± in front of the term on the right side of the equation.

Problem No. 34 - Solve x² = 50 using the square root property.

x = The square root of 50 has to be simplified. All perfect squares have to be taken out.

x = the answers

Problem No. 38 - Solve 3x² = 108 using the square root property.

First divide both sides of the equation by 3 and then take the square root of both sides.

3x² = 108 x² = 36 x = ±6 {±6} the answers

Problem No. 42 - Solve 5x² - 180 = 0 using the square root property.

First divide each term on both sides of the equation by 5 and then move the constant to the right side of the equation. The last step is to take the square root of both sides.

5x² - 180 = 0 x² - 36 = 0 x² = 36 x = ±6 {±6} the answers

Problem No. 46 - Solve using the square root property.

Notice the variable is in a binomial and it is isolated on one side of the equation and squared. Take the square root of both sides to solve the problem.

x - 4 = ± 15 x = 4 ± 15

x = 4 + 15 and x = 4 - 15

x = 19 and x = -11 {-11, 19} the answers

Problem No. 50 - Solve (x - 2)² = 7 using the square root property.

x - 2 = x = 2 {2 ± } the answers

Problem No. 52 - Solve x² - 10x + 25 = 121 using the square root property.

In this problem the left side of the equation must be factored first. It is a trinomial square and will factor into a binomial squared. Then take the square root of both sides.

x - 5 = ± 11