Question

pleasee help!
Solve. x2 - 8x = 20

What are the solutions of 4x2 - 3x - 5 = 0?

Answer 1

Simplifying
x2 + -8x = 20

Reorder the terms:
-8x + x2 = 20

Solving
-8x + x2 = 20

Solving for variable 'x'.

Reorder the terms:
-20 + -8x + x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + -8x + x2 = 0

Factor a trinomial.
(-2 + -1x)(10 + -1x) = 0

Subproblem 1Set the factor '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2
Subproblem 2Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10Solutionx = {-2, 10}

Answer 2

Simplifying
4x2 + -3x + -5 = 0

Reorder the terms:
-5 + -3x + 4x2 = 0

Solving
-5 + -3x + 4x2 = 0

Solving for variable 'x'.

Begin completing the square. Divide all terms by
4 the coefficient of the squared term:

Divide each side by '4'.
-1.25 + -0.75x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -0.75x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -0.75x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -0.75x + x2 = 0 + 1.25
-0.75x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-0.75x + x2 = 1.25

The x term is -0.75x. Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x + 0.140625 + x2 = 1.25 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = 1.25 + 0.140625

Combine like terms: 1.25 + 0.140625 = 1.390625
0.140625 + -0.75x + x2 = 1.390625

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 1.390625

Calculate the square root of the right side: 1.179247642

Break this problem into two subproblems by setting
(x + -0.375) equal to 1.179247642 and -1.179247642.

Subproblem 1x + -0.375 = 1.179247642

Simplifying
x + -0.375 = 1.179247642

Reorder the terms:
-0.375 + x = 1.179247642

Solving
-0.375 + x = 1.179247642

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = 1.179247642 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = 1.179247642 + 0.375
x = 1.179247642 + 0.375

Combine like terms: 1.179247642 + 0.375 = 1.554247642
x = 1.554247642

Simplifying
x = 1.554247642

Subproblem 2x + -0.375 = -1.179247642

Simplifying
x + -0.375 = -1.179247642

Reorder the terms:
-0.375 + x = -1.179247642

Solving
-0.375 + x = -1.179247642

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = -1.179247642 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = -1.179247642 + 0.375
x = -1.179247642 + 0.375

Combine like terms: -1.179247642 + 0.375 = -0.804247642
x = -0.804247642

Simplifying
x = -0.804247642

SolutionThe solution to the problem is based on the solutions
from the subproblems.
x = {1.554247642, -0.804247642}

Answer 3

thanks so much you are a lifesaver!