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Simplifying x(-4x + -13) = -1 Reorder the terms: x(-13 + -4x) = -1 (-13 * x + -4x * x) = -1 (-13x + -4x2) = -1 Solving -13x + -4x2 = -1 Solving for variable 'x'. Reorder the terms: 1 + -13x + -4x2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + -13x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.25 + 3.25x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 3.25x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 3.25x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 3.25x + x2 = 0 + 0.25 3.25x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 3.25x + x2 = 0.25 The x term is 3.25x. Take half its coefficient (1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. 3.25x + 2.640625 + x2 = 0.25 + 2.640625 Reorder the terms: 2.640625 + 3.25x + x2 = 0.25 + 2.640625 Combine like terms: 0.25 + 2.640625 = 2.890625 2.640625 + 3.25x + x2 = 2.890625 Factor a perfect square on the left side: (x + 1.625)(x + 1.625) = 2.890625 Calculate the square root of the right side: 1.700183814 Break this problem into two subproblems by setting (x + 1.625) equal to 1.700183814 and -1.700183814.Subproblem 1
x + 1.625 = 1.700183814 Simplifying x + 1.625 = 1.700183814 Reorder the terms: 1.625 + x = 1.700183814 Solving 1.625 + x = 1.700183814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = 1.700183814 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = 1.700183814 + -1.625 x = 1.700183814 + -1.625 Combine like terms: 1.700183814 + -1.625 = 0.075183814 x = 0.075183814 Simplifying x = 0.075183814Subproblem 2
x + 1.625 = -1.700183814 Simplifying x + 1.625 = -1.700183814 Reorder the terms: 1.625 + x = -1.700183814 Solving 1.625 + x = -1.700183814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = -1.700183814 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = -1.700183814 + -1.625 x = -1.700183814 + -1.625 Combine like terms: -1.700183814 + -1.625 = -3.325183814 x = -3.325183814 Simplifying x = -3.325183814Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.075183814, -3.325183814}
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