-16x^2+50x+4=0

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Solution for -16x^2+50x+4=0 equation:


Simplifying
-16x2 + 50x + 4 = 0

Reorder the terms:
4 + 50x + -16x2 = 0

Solving
4 + 50x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + 25x + -8x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(2 + 25x + -8x2)' equal to zero and attempt to solve: Simplifying 2 + 25x + -8x2 = 0 Solving 2 + 25x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.25 + -3.125x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -3.125x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -3.125x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -3.125x + x2 = 0 + 0.25 -3.125x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -3.125x + x2 = 0.25 The x term is -3.125x. Take half its coefficient (-1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. -3.125x + 2.44140625 + x2 = 0.25 + 2.44140625 Reorder the terms: 2.44140625 + -3.125x + x2 = 0.25 + 2.44140625 Combine like terms: 0.25 + 2.44140625 = 2.69140625 2.44140625 + -3.125x + x2 = 2.69140625 Factor a perfect square on the left side: (x + -1.5625)(x + -1.5625) = 2.69140625 Calculate the square root of the right side: 1.640550594 Break this problem into two subproblems by setting (x + -1.5625) equal to 1.640550594 and -1.640550594.

Subproblem 1

x + -1.5625 = 1.640550594 Simplifying x + -1.5625 = 1.640550594 Reorder the terms: -1.5625 + x = 1.640550594 Solving -1.5625 + x = 1.640550594 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + x = 1.640550594 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = 1.640550594 + 1.5625 x = 1.640550594 + 1.5625 Combine like terms: 1.640550594 + 1.5625 = 3.203050594 x = 3.203050594 Simplifying x = 3.203050594

Subproblem 2

x + -1.5625 = -1.640550594 Simplifying x + -1.5625 = -1.640550594 Reorder the terms: -1.5625 + x = -1.640550594 Solving -1.5625 + x = -1.640550594 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + x = -1.640550594 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = -1.640550594 + 1.5625 x = -1.640550594 + 1.5625 Combine like terms: -1.640550594 + 1.5625 = -0.078050594 x = -0.078050594 Simplifying x = -0.078050594

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.203050594, -0.078050594}

Solution

x = {3.203050594, -0.078050594}

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