4=64x-16x^2

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Solution for 4=64x-16x^2 equation:


Simplifying
4 = 64x + -16x2

Solving
4 = 64x + -16x2

Solving for variable 'x'.

Reorder the terms:
4 + -64x + 16x2 = 64x + -64x + -16x2 + 16x2

Combine like terms: 64x + -64x = 0
4 + -64x + 16x2 = 0 + -16x2 + 16x2
4 + -64x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
4 + -64x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + -16x + 4x2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(1 + -16x + 4x2)' equal to zero and attempt to solve: Simplifying 1 + -16x + 4x2 = 0 Solving 1 + -16x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + -4x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -4x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -4x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -4x + x2 = 0 + -0.25 -4x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -4x + x2 = -0.25 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 = -0.25 + 4 Reorder the terms: 4 + -4x + x2 = -0.25 + 4 Combine like terms: -0.25 + 4 = 3.75 4 + -4x + x2 = 3.75 Factor a perfect square on the left side: (x + -2)(x + -2) = 3.75 Calculate the square root of the right side: 1.936491673 Break this problem into two subproblems by setting (x + -2) equal to 1.936491673 and -1.936491673.

Subproblem 1

x + -2 = 1.936491673 Simplifying x + -2 = 1.936491673 Reorder the terms: -2 + x = 1.936491673 Solving -2 + x = 1.936491673 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 = 1.936491673 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.936491673 + 2 x = 1.936491673 + 2 Combine like terms: 1.936491673 + 2 = 3.936491673 x = 3.936491673 Simplifying x = 3.936491673

Subproblem 2

x + -2 = -1.936491673 Simplifying x + -2 = -1.936491673 Reorder the terms: -2 + x = -1.936491673 Solving -2 + x = -1.936491673 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 = -1.936491673 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.936491673 + 2 x = -1.936491673 + 2 Combine like terms: -1.936491673 + 2 = 0.063508327 x = 0.063508327 Simplifying x = 0.063508327

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.936491673, 0.063508327}

Solution

x = {3.936491673, 0.063508327}

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