16x^2+46x-26=0

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Solution for 16x^2+46x-26=0 equation:


Simplifying
16x2 + 46x + -26 = 0

Reorder the terms:
-26 + 46x + 16x2 = 0

Solving
-26 + 46x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-13 + 23x + 8x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-13 + 23x + 8x2)' equal to zero and attempt to solve: Simplifying -13 + 23x + 8x2 = 0 Solving -13 + 23x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.625 + 2.875x + x2 = 0 Move the constant term to the right: Add '1.625' to each side of the equation. -1.625 + 2.875x + 1.625 + x2 = 0 + 1.625 Reorder the terms: -1.625 + 1.625 + 2.875x + x2 = 0 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + 2.875x + x2 = 0 + 1.625 2.875x + x2 = 0 + 1.625 Combine like terms: 0 + 1.625 = 1.625 2.875x + x2 = 1.625 The x term is 2.875x. Take half its coefficient (1.4375). Square it (2.06640625) and add it to both sides. Add '2.06640625' to each side of the equation. 2.875x + 2.06640625 + x2 = 1.625 + 2.06640625 Reorder the terms: 2.06640625 + 2.875x + x2 = 1.625 + 2.06640625 Combine like terms: 1.625 + 2.06640625 = 3.69140625 2.06640625 + 2.875x + x2 = 3.69140625 Factor a perfect square on the left side: (x + 1.4375)(x + 1.4375) = 3.69140625 Calculate the square root of the right side: 1.921303269 Break this problem into two subproblems by setting (x + 1.4375) equal to 1.921303269 and -1.921303269.

Subproblem 1

x + 1.4375 = 1.921303269 Simplifying x + 1.4375 = 1.921303269 Reorder the terms: 1.4375 + x = 1.921303269 Solving 1.4375 + x = 1.921303269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4375' to each side of the equation. 1.4375 + -1.4375 + x = 1.921303269 + -1.4375 Combine like terms: 1.4375 + -1.4375 = 0.0000 0.0000 + x = 1.921303269 + -1.4375 x = 1.921303269 + -1.4375 Combine like terms: 1.921303269 + -1.4375 = 0.483803269 x = 0.483803269 Simplifying x = 0.483803269

Subproblem 2

x + 1.4375 = -1.921303269 Simplifying x + 1.4375 = -1.921303269 Reorder the terms: 1.4375 + x = -1.921303269 Solving 1.4375 + x = -1.921303269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4375' to each side of the equation. 1.4375 + -1.4375 + x = -1.921303269 + -1.4375 Combine like terms: 1.4375 + -1.4375 = 0.0000 0.0000 + x = -1.921303269 + -1.4375 x = -1.921303269 + -1.4375 Combine like terms: -1.921303269 + -1.4375 = -3.358803269 x = -3.358803269 Simplifying x = -3.358803269

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.483803269, -3.358803269}

Solution

x = {0.483803269, -3.358803269}

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