7+16x-4x^2=0

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Solution for 7+16x-4x^2=0 equation:


Simplifying
7 + 16x + -4x2 = 0

Solving
7 + 16x + -4x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-1.75 + -4x + x2 = 0

Move the constant term to the right:

Add '1.75' to each side of the equation.
-1.75 + -4x + 1.75 + x2 = 0 + 1.75

Reorder the terms:
-1.75 + 1.75 + -4x + x2 = 0 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + -4x + x2 = 0 + 1.75
-4x + x2 = 0 + 1.75

Combine like terms: 0 + 1.75 = 1.75
-4x + x2 = 1.75

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 = 1.75 + 4

Reorder the terms:
4 + -4x + x2 = 1.75 + 4

Combine like terms: 1.75 + 4 = 5.75
4 + -4x + x2 = 5.75

Factor a perfect square on the left side:
(x + -2)(x + -2) = 5.75

Calculate the square root of the right side: 2.397915762

Break this problem into two subproblems by setting 
(x + -2) equal to 2.397915762 and -2.397915762.

Subproblem 1

x + -2 = 2.397915762 Simplifying x + -2 = 2.397915762 Reorder the terms: -2 + x = 2.397915762 Solving -2 + x = 2.397915762 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 = 2.397915762 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.397915762 + 2 x = 2.397915762 + 2 Combine like terms: 2.397915762 + 2 = 4.397915762 x = 4.397915762 Simplifying x = 4.397915762

Subproblem 2

x + -2 = -2.397915762 Simplifying x + -2 = -2.397915762 Reorder the terms: -2 + x = -2.397915762 Solving -2 + x = -2.397915762 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 = -2.397915762 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.397915762 + 2 x = -2.397915762 + 2 Combine like terms: -2.397915762 + 2 = -0.397915762 x = -0.397915762 Simplifying x = -0.397915762

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.397915762, -0.397915762}

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