solve equations (a) x2+5x-120=0 (b) 8x2+7x-120=0 (c) x2+2x-120=0
Answers
Answer:
(i) (x + 1)2 = 2(x – 3)
=> x2 + 2x + 1 = 2x – 6
=> x2 + 2x + 1 - 2x + 6 = 0
=> x2 + 7 = 0
=> x2 + 0x + 7 = 0
This is an equation of the form ax2 + bx + c = 0
Hence, the given equation is a quadratic equation.
(ii) x2 – 2x = (–2) (3 – x)
=> x2 – 2x = -6 + 2x
=> x2 -2x – 2x + 6 = 0
=> x2 – 4x + 6 = 0
This is an equation of the form ax2 + bx + c = 0
Hence, the given equation is a quadratic equation.
(iii) (x – 2)(x + 1) = (x – 1)(x + 3)
=> x2 – 2x + x – 2 = x2 – x + 3x – 3
=> x2 – x – 2 = x2 + 2x – 3
=> x2 – x – 2 - x2 - 2x + 3 = 0
=> -3x + 1 = 0
=> 3x – 1 = 0
This is not an equation of the form ax2 + bx + c = 0
Hence, the given equation is not a quadratic equation.
Answer:
Simplifying
x2 + -5x + -120 = 0
Reorder the terms:
-120 + -5x + x2 = 0
Solving
-120 + -5x + x2 = 0
Solving for variable 'x'.
Begin completing the square.
Move the constant term to the right:
Add '120' to each side of the equation.
-120 + -5x + 120 + x2 = 0 + 120
Reorder the terms:
-120 + 120 + -5x + x2 = 0 + 120
Combine like terms: -120 + 120 = 0
0 + -5x + x2 = 0 + 120
-5x + x2 = 0 + 120
Combine like terms: 0 + 120 = 120
-5x + x2 = 120
The x term is -5x. Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.
Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 120 + 6.25
Reorder the terms:
6.25 + -5x + x2 = 120 + 6.25
Combine like terms: 120 + 6.25 = 126.25
6.25 + -5x + x2 = 126.25
Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 126.25
Calculate the square root of the right side: 11.236102527
Break this problem into two subproblems by setting
(x + -2.5) equal to 11.236102527 and -11.236102527.
Subproblem 1
x + -2.5 = 11.236102527
Simplifying
x + -2.5 = 11.236102527
Reorder the terms:
-2.5 + x = 11.236102527
Solving
-2.5 + x = 11.236102527
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 11.236102527 + 2.5
Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 11.236102527 + 2.5
x = 11.236102527 + 2.5
Combine like terms: 11.236102527 + 2.5 = 13.736102527
x = 13.736102527
Simplifying
x = 13.736102527