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Simplifying x(-2x + -13) = -2 Reorder the terms: x(-13 + -2x) = -2 (-13 * x + -2x * x) = -2 (-13x + -2x2) = -2 Solving -13x + -2x2 = -2 Solving for variable 'x'. Reorder the terms: 2 + -13x + -2x2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + -13x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -1 + 6.5x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 6.5x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 6.5x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 6.5x + x2 = 0 + 1 6.5x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 6.5x + x2 = 1 The x term is 6.5x. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5x + 10.5625 + x2 = 1 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = 1 + 10.5625 Combine like terms: 1 + 10.5625 = 11.5625 10.5625 + 6.5x + x2 = 11.5625 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 11.5625 Calculate the square root of the right side: 3.400367627 Break this problem into two subproblems by setting (x + 3.25) equal to 3.400367627 and -3.400367627.Subproblem 1
x + 3.25 = 3.400367627 Simplifying x + 3.25 = 3.400367627 Reorder the terms: 3.25 + x = 3.400367627 Solving 3.25 + x = 3.400367627 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = 3.400367627 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 3.400367627 + -3.25 x = 3.400367627 + -3.25 Combine like terms: 3.400367627 + -3.25 = 0.150367627 x = 0.150367627 Simplifying x = 0.150367627Subproblem 2
x + 3.25 = -3.400367627 Simplifying x + 3.25 = -3.400367627 Reorder the terms: 3.25 + x = -3.400367627 Solving 3.25 + x = -3.400367627 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = -3.400367627 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -3.400367627 + -3.25 x = -3.400367627 + -3.25 Combine like terms: -3.400367627 + -3.25 = -6.650367627 x = -6.650367627 Simplifying x = -6.650367627Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.150367627, -6.650367627}
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