0=16x^2+62x+2

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Solution for 0=16x^2+62x+2 equation:


Simplifying
0 = 16x2 + 62x + 2

Reorder the terms:
0 = 2 + 62x + 16x2

Solving
0 = 2 + 62x + 16x2

Solving for variable 'x'.

Combine like terms: 0 + -2 = -2
-2 + -62x + -16x2 = 2 + 62x + 16x2 + -2 + -62x + -16x2

Reorder the terms:
-2 + -62x + -16x2 = 2 + -2 + 62x + -62x + 16x2 + -16x2

Combine like terms: 2 + -2 = 0
-2 + -62x + -16x2 = 0 + 62x + -62x + 16x2 + -16x2
-2 + -62x + -16x2 = 62x + -62x + 16x2 + -16x2

Combine like terms: 62x + -62x = 0
-2 + -62x + -16x2 = 0 + 16x2 + -16x2
-2 + -62x + -16x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
-2 + -62x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(1 + 31x + 8x2) = 0

Ignore the factor -2.

Subproblem 1

Set the factor '(1 + 31x + 8x2)' equal to zero and attempt to solve: Simplifying 1 + 31x + 8x2 = 0 Solving 1 + 31x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.125 + 3.875x + x2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + 3.875x + -0.125 + x2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + 3.875x + x2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + 3.875x + x2 = 0 + -0.125 3.875x + x2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 3.875x + x2 = -0.125 The x term is 3.875x. Take half its coefficient (1.9375). Square it (3.75390625) and add it to both sides. Add '3.75390625' to each side of the equation. 3.875x + 3.75390625 + x2 = -0.125 + 3.75390625 Reorder the terms: 3.75390625 + 3.875x + x2 = -0.125 + 3.75390625 Combine like terms: -0.125 + 3.75390625 = 3.62890625 3.75390625 + 3.875x + x2 = 3.62890625 Factor a perfect square on the left side: (x + 1.9375)(x + 1.9375) = 3.62890625 Calculate the square root of the right side: 1.904968832 Break this problem into two subproblems by setting (x + 1.9375) equal to 1.904968832 and -1.904968832.

Subproblem 1

x + 1.9375 = 1.904968832 Simplifying x + 1.9375 = 1.904968832 Reorder the terms: 1.9375 + x = 1.904968832 Solving 1.9375 + x = 1.904968832 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9375' to each side of the equation. 1.9375 + -1.9375 + x = 1.904968832 + -1.9375 Combine like terms: 1.9375 + -1.9375 = 0.0000 0.0000 + x = 1.904968832 + -1.9375 x = 1.904968832 + -1.9375 Combine like terms: 1.904968832 + -1.9375 = -0.032531168 x = -0.032531168 Simplifying x = -0.032531168

Subproblem 2

x + 1.9375 = -1.904968832 Simplifying x + 1.9375 = -1.904968832 Reorder the terms: 1.9375 + x = -1.904968832 Solving 1.9375 + x = -1.904968832 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9375' to each side of the equation. 1.9375 + -1.9375 + x = -1.904968832 + -1.9375 Combine like terms: 1.9375 + -1.9375 = 0.0000 0.0000 + x = -1.904968832 + -1.9375 x = -1.904968832 + -1.9375 Combine like terms: -1.904968832 + -1.9375 = -3.842468832 x = -3.842468832 Simplifying x = -3.842468832

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.032531168, -3.842468832}

Solution

x = {-0.032531168, -3.842468832}

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