-16x^2+16x+46=0

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


Simplifying
-16x2 + 16x + 46 = 0

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

Solving
46 + 16x + -16x2 = 0

Solving for variable 'x'.

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

Ignore the factor 2.

Subproblem 1

Set the factor '(23 + 8x + -8x2)' equal to zero and attempt to solve: Simplifying 23 + 8x + -8x2 = 0 Solving 23 + 8x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -2.875 + -1x + x2 = 0 Move the constant term to the right: Add '2.875' to each side of the equation. -2.875 + -1x + 2.875 + x2 = 0 + 2.875 Reorder the terms: -2.875 + 2.875 + -1x + x2 = 0 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + -1x + x2 = 0 + 2.875 -1x + x2 = 0 + 2.875 Combine like terms: 0 + 2.875 = 2.875 -1x + x2 = 2.875 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 2.875 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 2.875 + 0.25 Combine like terms: 2.875 + 0.25 = 3.125 0.25 + -1x + x2 = 3.125 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 3.125 Calculate the square root of the right side: 1.767766953 Break this problem into two subproblems by setting (x + -0.5) equal to 1.767766953 and -1.767766953.

Subproblem 1

x + -0.5 = 1.767766953 Simplifying x + -0.5 = 1.767766953 Reorder the terms: -0.5 + x = 1.767766953 Solving -0.5 + x = 1.767766953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.767766953 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.767766953 + 0.5 x = 1.767766953 + 0.5 Combine like terms: 1.767766953 + 0.5 = 2.267766953 x = 2.267766953 Simplifying x = 2.267766953

Subproblem 2

x + -0.5 = -1.767766953 Simplifying x + -0.5 = -1.767766953 Reorder the terms: -0.5 + x = -1.767766953 Solving -0.5 + x = -1.767766953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.767766953 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.767766953 + 0.5 x = -1.767766953 + 0.5 Combine like terms: -1.767766953 + 0.5 = -1.267766953 x = -1.267766953 Simplifying x = -1.267766953

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.267766953, -1.267766953}

Solution

x = {2.267766953, -1.267766953}

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