2x^2-14x=1224

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Solution for 2x^2-14x=1224 equation:


Simplifying
2x2 + -14x = 1224

Reorder the terms:
-14x + 2x2 = 1224

Solving
-14x + 2x2 = 1224

Solving for variable 'x'.

Reorder the terms:
-1224 + -14x + 2x2 = 1224 + -1224

Combine like terms: 1224 + -1224 = 0
-1224 + -14x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-612 + -7x + x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-612 + -7x + x2)' equal to zero and attempt to solve: Simplifying -612 + -7x + x2 = 0 Solving -612 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '612' to each side of the equation. -612 + -7x + 612 + x2 = 0 + 612 Reorder the terms: -612 + 612 + -7x + x2 = 0 + 612 Combine like terms: -612 + 612 = 0 0 + -7x + x2 = 0 + 612 -7x + x2 = 0 + 612 Combine like terms: 0 + 612 = 612 -7x + x2 = 612 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 612 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 612 + 12.25 Combine like terms: 612 + 12.25 = 624.25 12.25 + -7x + x2 = 624.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 624.25 Calculate the square root of the right side: 24.984995497 Break this problem into two subproblems by setting (x + -3.5) equal to 24.984995497 and -24.984995497.

Subproblem 1

x + -3.5 = 24.984995497 Simplifying x + -3.5 = 24.984995497 Reorder the terms: -3.5 + x = 24.984995497 Solving -3.5 + x = 24.984995497 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 24.984995497 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 24.984995497 + 3.5 x = 24.984995497 + 3.5 Combine like terms: 24.984995497 + 3.5 = 28.484995497 x = 28.484995497 Simplifying x = 28.484995497

Subproblem 2

x + -3.5 = -24.984995497 Simplifying x + -3.5 = -24.984995497 Reorder the terms: -3.5 + x = -24.984995497 Solving -3.5 + x = -24.984995497 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -24.984995497 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -24.984995497 + 3.5 x = -24.984995497 + 3.5 Combine like terms: -24.984995497 + 3.5 = -21.484995497 x = -21.484995497 Simplifying x = -21.484995497

Solution

The solution to the problem is based on the solutions from the subproblems. x = {28.484995497, -21.484995497}

Solution

x = {28.484995497, -21.484995497}

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