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31 October, 20:35

3x2 + 5x - 7x + 3 - 5x2 + 2

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  1. 31 October, 22:41
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    Simplifying

    3x2 + 5x + - 7x + 3 + - 5x2 + 2 = 0

    Reorder the terms:

    3 + 2 + 5x + - 7x + 3x2 + - 5x2 = 0

    Combine like terms: 3 + 2 = 5

    5 + 5x + - 7x + 3x2 + - 5x2 = 0

    Combine like terms: 5x + - 7x = - 2x

    5 + - 2x + 3x2 + - 5x2 = 0

    Combine like terms: 3x2 + - 5x2 = - 2x2

    5 + - 2x + - 2x2 = 0

    Solving

    5 + - 2x + - 2x2 = 0

    Solving for variable 'x'.

    Begin completing the square. Divide all terms by

    -2 the coefficient of the squared term:

    Divide each side by '-2'.

    -2.5 + x + x2 = 0

    Move the constant term to the right:

    Add '2.5' to each side of the equation.

    -2.5 + x + 2.5 + x2 = 0 + 2.5

    Reorder the terms:

    -2.5 + 2.5 + x + x2 = 0 + 2.5

    Combine like terms: - 2.5 + 2.5 = 0.0

    0.0 + x + x2 = 0 + 2.5

    x + x2 = 0 + 2.5

    Combine like terms: 0 + 2.5 = 2.5

    x + x2 = 2.5

    The x term is x. Take half its coefficient (0.5).

    Square it (0.25) and add it to both sides.

    Add '0.25' to each side of the equation.

    + 0.25 + x2 = 2.5 + 0.25

    Combine like terms: + 0.25 = 1.25

    1.25 + x2 = 2.5 + 0.25

    Combine like terms: 2.5 + 0.25 = 2.75

    1.25 + x2 = 2.75

    Factor a perfect square on the left side:

    (x + 0.5) (x + 0.5) = 2.75

    Calculate the square root of the right side: 1.658312395

    Break this problem into two subproblems by setting

    (x + 0.5) equal to 1.658312395 and - 1.658312395.

    Subproblem 1

    x + 0.5 = 1.658312395

    Simplifying

    x + 0.5 = 1.658312395

    Reorder the terms:

    0.5 + x = 1.658312395

    Solving

    0.5 + x = 1.658312395

    Solving for variable 'x'.

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

    Add '-0.5' to each side of the equation.

    0.5 + - 0.5 + x = 1.658312395 + - 0.5

    Combine like terms: 0.5 + - 0.5 = 0.0

    0.0 + x = 1.658312395 + - 0.5

    x = 1.658312395 + - 0.5

    Combine like terms: 1.658312395 + - 0.5 = 1.158312395

    x = 1.158312395

    Simplifying

    x = 1.158312395

    Subproblem 2

    x + 0.5 = - 1.658312395

    Simplifying

    x + 0.5 = - 1.658312395

    Reorder the terms:

    0.5 + x = - 1.658312395

    Solving

    0.5 + x = - 1.658312395

    Solving for variable 'x'.

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

    Add '-0.5' to each side of the equation.

    0.5 + - 0.5 + x = - 1.658312395 + - 0.5

    Combine like terms: 0.5 + - 0.5 = 0.0

    0.0 + x = - 1.658312395 + - 0.5

    x = - 1.658312395 + - 0.5

    Combine like terms: - 1.658312395 + - 0.5 = - 2.158312395

    x = - 2.158312395

    Simplifying

    x = - 2.158312395

    Solution

    The solution to the problem is based on the solutions

    from the subproblems.

    x = {1.158312395, - 2.158312395}
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