Completing the square method is a technique for find the solutions of a quadratic equation of the form ax^2 + bx + c = 0. This method involves completing the square of the quadratic expression to the form (x + d)^2 = e, where d and e are constants. Find the values of x, which satisfy the inequation: − 2 ≤ 1 2 − 2 x 3 < 1 5 6, x ∈ N Graph the solution set on the real number line. 03:19 View Solution This is how the solution of the equation 2 x 2 − 12 x + 18 = 0 goes: 2 x 2 − 12 x + 18 = 0 x 2 − 6 x + 9 = 0 Divide by 2. ( x − 3) 2 = 0 Factor. ↓ x − 3 = 0 x = 3. All terms originally had a common factor of 2 , so we divided all sides by 2 —the zero side remained zero—which made the factorization easier. Draw a vertical line and write the constants to the right of the line. Example 5.4.1 5.4. 1: Writing the Augmented Matrix for a System of Equations. Write the augmented matrix for the given system of equations. x + 2y − z 2x − y + 2z x − 3y + 3z = 3 = 6 = 4 x + 2 y − z = 3 2 x − y + 2 z = 6 x − 3 y + 3 z = 4. Solution. 2x − 3 = 5x + 6 2 x - 3 = 5 x + 6. Move all terms containing x x to the left side of the equation. Tap for more steps −3x− 3 = 6 - 3 x - 3 = 6. Move all terms not containing x x to the right side of the equation. Tap for more steps −3x = 9 - 3 x = 9. Divide each term in −3x = 9 - 3 x = 9 by −3 - 3 and simplify. elimination\:x+2y=2x-5,\:x-y=3 ; Show More; Description. Solve simultaneous equations step-by-step. Frequently Asked Questions (FAQ) How to solve linear Simultaneous equations with two variables by graphing? To solve linear simultaneous equations with two variables by graphing, plot both equations on the same set of axes. The coordinates of the Graph 2x+3y=6. 2x + 3y = 6 2 x + 3 y = 6. Solve for y y. Tap for more steps y = 2− 2x 3 y = 2 - 2 x 3. Rewrite in slope-intercept form. Tap for more steps y = − 2 3x+2 y = - 2 3 x + 2. Use the slope-intercept form to find the slope and y-intercept. Example 1 Solve for x and check: x + 5 = 3. Solution. Using the same procedures learned in chapter 2, we subtract 5 from each side of the equation obtaining. Example 5 Solve for x and graph the solution: -2x>6. Solution. To obtain x on the left side we must divide each term by - 2. Notice that since we are dividing by a negative number, we Simplify (2x-3) (3x-5) (2x − 3) (3x − 5) ( 2 x - 3) ( 3 x - 5) Expand (2x−3)(3x− 5) ( 2 x - 3) ( 3 x - 5) using the FOIL Method. Tap for more steps 2x(3x)+2x⋅−5−3(3x)− 3⋅−5 2 x ( 3 x) + 2 x ⋅ - 5 - 3 ( 3 x) - 3 ⋅ - 5. Simplify and combine like terms. Tap for more steps 6x2 − 19x+15 6 x 2 - 19 x + 15. Free math Use the rational zero theorem and synthetic division to find all the possible rational zeros of the polynomial. f (x)=x 3 −2x 2 −x+2. Solution. From the rational zero theorem, p q p q is a rational zero of the polynomial f. So p is a divisor of 2 and q is a divisor of 1. Hence, p can take the following values: -1, 1, -2, 2 and q can be Ujh5N.