864=2x^2+8x-24

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Solution for 864=2x^2+8x-24 equation:


Simplifying
864 = 2x2 + 8x + -24

Reorder the terms:
864 = -24 + 8x + 2x2

Solving
864 = -24 + 8x + 2x2

Solving for variable 'x'.

Combine like terms: 864 + 24 = 888
888 + -8x + -2x2 = -24 + 8x + 2x2 + 24 + -8x + -2x2

Reorder the terms:
888 + -8x + -2x2 = -24 + 24 + 8x + -8x + 2x2 + -2x2

Combine like terms: -24 + 24 = 0
888 + -8x + -2x2 = 0 + 8x + -8x + 2x2 + -2x2
888 + -8x + -2x2 = 8x + -8x + 2x2 + -2x2

Combine like terms: 8x + -8x = 0
888 + -8x + -2x2 = 0 + 2x2 + -2x2
888 + -8x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
888 + -8x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(444 + -4x + -1x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(444 + -4x + -1x2)' equal to zero and attempt to solve: Simplifying 444 + -4x + -1x2 = 0 Solving 444 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -444 + 4x + x2 = 0 Move the constant term to the right: Add '444' to each side of the equation. -444 + 4x + 444 + x2 = 0 + 444 Reorder the terms: -444 + 444 + 4x + x2 = 0 + 444 Combine like terms: -444 + 444 = 0 0 + 4x + x2 = 0 + 444 4x + x2 = 0 + 444 Combine like terms: 0 + 444 = 444 4x + x2 = 444 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 444 + 4 Reorder the terms: 4 + 4x + x2 = 444 + 4 Combine like terms: 444 + 4 = 448 4 + 4x + x2 = 448 Factor a perfect square on the left side: (x + 2)(x + 2) = 448 Calculate the square root of the right side: 21.166010489 Break this problem into two subproblems by setting (x + 2) equal to 21.166010489 and -21.166010489.

Subproblem 1

x + 2 = 21.166010489 Simplifying x + 2 = 21.166010489 Reorder the terms: 2 + x = 21.166010489 Solving 2 + x = 21.166010489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 21.166010489 + -2 Combine like terms: 2 + -2 = 0 0 + x = 21.166010489 + -2 x = 21.166010489 + -2 Combine like terms: 21.166010489 + -2 = 19.166010489 x = 19.166010489 Simplifying x = 19.166010489

Subproblem 2

x + 2 = -21.166010489 Simplifying x + 2 = -21.166010489 Reorder the terms: 2 + x = -21.166010489 Solving 2 + x = -21.166010489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -21.166010489 + -2 Combine like terms: 2 + -2 = 0 0 + x = -21.166010489 + -2 x = -21.166010489 + -2 Combine like terms: -21.166010489 + -2 = -23.166010489 x = -23.166010489 Simplifying x = -23.166010489

Solution

The solution to the problem is based on the solutions from the subproblems. x = {19.166010489, -23.166010489}

Solution

x = {19.166010489, -23.166010489}

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