(3x^2-5x+7)-(5x^2-9x-1)=

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Solution for (3x^2-5x+7)-(5x^2-9x-1)= equation:


Simplifying
(3x2 + -5x + 7) + -1(5x2 + -9x + -1) = 0

Reorder the terms:
(7 + -5x + 3x2) + -1(5x2 + -9x + -1) = 0

Remove parenthesis around (7 + -5x + 3x2)
7 + -5x + 3x2 + -1(5x2 + -9x + -1) = 0

Reorder the terms:
7 + -5x + 3x2 + -1(-1 + -9x + 5x2) = 0
7 + -5x + 3x2 + (-1 * -1 + -9x * -1 + 5x2 * -1) = 0
7 + -5x + 3x2 + (1 + 9x + -5x2) = 0

Reorder the terms:
7 + 1 + -5x + 9x + 3x2 + -5x2 = 0

Combine like terms: 7 + 1 = 8
8 + -5x + 9x + 3x2 + -5x2 = 0

Combine like terms: -5x + 9x = 4x
8 + 4x + 3x2 + -5x2 = 0

Combine like terms: 3x2 + -5x2 = -2x2
8 + 4x + -2x2 = 0

Solving
8 + 4x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 2x + -1x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(4 + 2x + -1x2)' equal to zero and attempt to solve: Simplifying 4 + 2x + -1x2 = 0 Solving 4 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + -2x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -2x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -2x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -2x + x2 = 0 + 4 -2x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -2x + x2 = 4 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 4 + 1 Reorder the terms: 1 + -2x + x2 = 4 + 1 Combine like terms: 4 + 1 = 5 1 + -2x + x2 = 5 Factor a perfect square on the left side: (x + -1)(x + -1) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x + -1) equal to 2.236067978 and -2.236067978.

Subproblem 1

x + -1 = 2.236067978 Simplifying x + -1 = 2.236067978 Reorder the terms: -1 + x = 2.236067978 Solving -1 + x = 2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.236067978 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.236067978 + 1 x = 2.236067978 + 1 Combine like terms: 2.236067978 + 1 = 3.236067978 x = 3.236067978 Simplifying x = 3.236067978

Subproblem 2

x + -1 = -2.236067978 Simplifying x + -1 = -2.236067978 Reorder the terms: -1 + x = -2.236067978 Solving -1 + x = -2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.236067978 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.236067978 + 1 x = -2.236067978 + 1 Combine like terms: -2.236067978 + 1 = -1.236067978 x = -1.236067978 Simplifying x = -1.236067978

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.236067978, -1.236067978}

Solution

x = {3.236067978, -1.236067978}

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