8+14x-50x^2=0

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Solution for 8+14x-50x^2=0 equation:


Simplifying
8 + 14x + -50x2 = 0

Solving
8 + 14x + -50x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 7x + -25x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(4 + 7x + -25x2)' equal to zero and attempt to solve: Simplifying 4 + 7x + -25x2 = 0 Solving 4 + 7x + -25x2 = 0 Begin completing the square. Divide all terms by -25 the coefficient of the squared term: Divide each side by '-25'. -0.16 + -0.28x + x2 = 0 Move the constant term to the right: Add '0.16' to each side of the equation. -0.16 + -0.28x + 0.16 + x2 = 0 + 0.16 Reorder the terms: -0.16 + 0.16 + -0.28x + x2 = 0 + 0.16 Combine like terms: -0.16 + 0.16 = 0.00 0.00 + -0.28x + x2 = 0 + 0.16 -0.28x + x2 = 0 + 0.16 Combine like terms: 0 + 0.16 = 0.16 -0.28x + x2 = 0.16 The x term is -0.28x. Take half its coefficient (-0.14). Square it (0.0196) and add it to both sides. Add '0.0196' to each side of the equation. -0.28x + 0.0196 + x2 = 0.16 + 0.0196 Reorder the terms: 0.0196 + -0.28x + x2 = 0.16 + 0.0196 Combine like terms: 0.16 + 0.0196 = 0.1796 0.0196 + -0.28x + x2 = 0.1796 Factor a perfect square on the left side: (x + -0.14)(x + -0.14) = 0.1796 Calculate the square root of the right side: 0.423792402 Break this problem into two subproblems by setting (x + -0.14) equal to 0.423792402 and -0.423792402.

Subproblem 1

x + -0.14 = 0.423792402 Simplifying x + -0.14 = 0.423792402 Reorder the terms: -0.14 + x = 0.423792402 Solving -0.14 + x = 0.423792402 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.14' to each side of the equation. -0.14 + 0.14 + x = 0.423792402 + 0.14 Combine like terms: -0.14 + 0.14 = 0.00 0.00 + x = 0.423792402 + 0.14 x = 0.423792402 + 0.14 Combine like terms: 0.423792402 + 0.14 = 0.563792402 x = 0.563792402 Simplifying x = 0.563792402

Subproblem 2

x + -0.14 = -0.423792402 Simplifying x + -0.14 = -0.423792402 Reorder the terms: -0.14 + x = -0.423792402 Solving -0.14 + x = -0.423792402 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.14' to each side of the equation. -0.14 + 0.14 + x = -0.423792402 + 0.14 Combine like terms: -0.14 + 0.14 = 0.00 0.00 + x = -0.423792402 + 0.14 x = -0.423792402 + 0.14 Combine like terms: -0.423792402 + 0.14 = -0.283792402 x = -0.283792402 Simplifying x = -0.283792402

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.563792402, -0.283792402}

Solution

x = {0.563792402, -0.283792402}

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