80+14x-2x^2=0

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Solution for 80+14x-2x^2=0 equation:


Simplifying
80 + 14x + -2x2 = 0

Solving
80 + 14x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(40 + 7x + -1x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(40 + 7x + -1x2)' equal to zero and attempt to solve: Simplifying 40 + 7x + -1x2 = 0 Solving 40 + 7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -40 + -7x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + -7x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + -7x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -7x + x2 = 0 + 40 -7x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 -7x + x2 = 40 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 = 40 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 40 + 12.25 Combine like terms: 40 + 12.25 = 52.25 12.25 + -7x + x2 = 52.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 52.25 Calculate the square root of the right side: 7.228416147 Break this problem into two subproblems by setting (x + -3.5) equal to 7.228416147 and -7.228416147.

Subproblem 1

x + -3.5 = 7.228416147 Simplifying x + -3.5 = 7.228416147 Reorder the terms: -3.5 + x = 7.228416147 Solving -3.5 + x = 7.228416147 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 = 7.228416147 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 7.228416147 + 3.5 x = 7.228416147 + 3.5 Combine like terms: 7.228416147 + 3.5 = 10.728416147 x = 10.728416147 Simplifying x = 10.728416147

Subproblem 2

x + -3.5 = -7.228416147 Simplifying x + -3.5 = -7.228416147 Reorder the terms: -3.5 + x = -7.228416147 Solving -3.5 + x = -7.228416147 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 = -7.228416147 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -7.228416147 + 3.5 x = -7.228416147 + 3.5 Combine like terms: -7.228416147 + 3.5 = -3.728416147 x = -3.728416147 Simplifying x = -3.728416147

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.728416147, -3.728416147}

Solution

x = {10.728416147, -3.728416147}

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