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Simplifying 5x(4x + -1) = 2 Reorder the terms: 5x(-1 + 4x) = 2 (-1 * 5x + 4x * 5x) = 2 (-5x + 20x2) = 2 Solving -5x + 20x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + -5x + 20x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -5x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.1 + -0.25x + x2 = 0.0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + -0.25x + 0.1 + x2 = 0.0 + 0.1 Reorder the terms: -0.1 + 0.1 + -0.25x + x2 = 0.0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + -0.25x + x2 = 0.0 + 0.1 -0.25x + x2 = 0.0 + 0.1 Combine like terms: 0.0 + 0.1 = 0.1 -0.25x + x2 = 0.1 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 0.1 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 0.1 + 0.015625 Combine like terms: 0.1 + 0.015625 = 0.115625 0.015625 + -0.25x + x2 = 0.115625 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 0.115625 Calculate the square root of the right side: 0.340036763 Break this problem into two subproblems by setting (x + -0.125) equal to 0.340036763 and -0.340036763.Subproblem 1
x + -0.125 = 0.340036763 Simplifying x + -0.125 = 0.340036763 Reorder the terms: -0.125 + x = 0.340036763 Solving -0.125 + x = 0.340036763 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 0.340036763 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 0.340036763 + 0.125 x = 0.340036763 + 0.125 Combine like terms: 0.340036763 + 0.125 = 0.465036763 x = 0.465036763 Simplifying x = 0.465036763Subproblem 2
x + -0.125 = -0.340036763 Simplifying x + -0.125 = -0.340036763 Reorder the terms: -0.125 + x = -0.340036763 Solving -0.125 + x = -0.340036763 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -0.340036763 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -0.340036763 + 0.125 x = -0.340036763 + 0.125 Combine like terms: -0.340036763 + 0.125 = -0.215036763 x = -0.215036763 Simplifying x = -0.215036763Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.465036763, -0.215036763}
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