24x-2x^2+678=0

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Solution for 24x-2x^2+678=0 equation:


Simplifying
24x + -2x2 + 678 = 0

Reorder the terms:
678 + 24x + -2x2 = 0

Solving
678 + 24x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(339 + 12x + -1x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(339 + 12x + -1x2)' equal to zero and attempt to solve: Simplifying 339 + 12x + -1x2 = 0 Solving 339 + 12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -339 + -12x + x2 = 0 Move the constant term to the right: Add '339' to each side of the equation. -339 + -12x + 339 + x2 = 0 + 339 Reorder the terms: -339 + 339 + -12x + x2 = 0 + 339 Combine like terms: -339 + 339 = 0 0 + -12x + x2 = 0 + 339 -12x + x2 = 0 + 339 Combine like terms: 0 + 339 = 339 -12x + x2 = 339 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 339 + 36 Reorder the terms: 36 + -12x + x2 = 339 + 36 Combine like terms: 339 + 36 = 375 36 + -12x + x2 = 375 Factor a perfect square on the left side: (x + -6)(x + -6) = 375 Calculate the square root of the right side: 19.364916731 Break this problem into two subproblems by setting (x + -6) equal to 19.364916731 and -19.364916731.

Subproblem 1

x + -6 = 19.364916731 Simplifying x + -6 = 19.364916731 Reorder the terms: -6 + x = 19.364916731 Solving -6 + x = 19.364916731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 19.364916731 + 6 Combine like terms: -6 + 6 = 0 0 + x = 19.364916731 + 6 x = 19.364916731 + 6 Combine like terms: 19.364916731 + 6 = 25.364916731 x = 25.364916731 Simplifying x = 25.364916731

Subproblem 2

x + -6 = -19.364916731 Simplifying x + -6 = -19.364916731 Reorder the terms: -6 + x = -19.364916731 Solving -6 + x = -19.364916731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -19.364916731 + 6 Combine like terms: -6 + 6 = 0 0 + x = -19.364916731 + 6 x = -19.364916731 + 6 Combine like terms: -19.364916731 + 6 = -13.364916731 x = -13.364916731 Simplifying x = -13.364916731

Solution

The solution to the problem is based on the solutions from the subproblems. x = {25.364916731, -13.364916731}

Solution

x = {25.364916731, -13.364916731}

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