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Simplifying x(-2x + -13) = -3 Reorder the terms: x(-13 + -2x) = -3 (-13 * x + -2x * x) = -3 (-13x + -2x2) = -3 Solving -13x + -2x2 = -3 Solving for variable 'x'. Reorder the terms: 3 + -13x + -2x2 = -3 + 3 Combine like terms: -3 + 3 = 0 3 + -13x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -1.5 + 6.5x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 6.5x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 6.5x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 6.5x + x2 = 0 + 1.5 6.5x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 6.5x + x2 = 1.5 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 = 1.5 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = 1.5 + 10.5625 Combine like terms: 1.5 + 10.5625 = 12.0625 10.5625 + 6.5x + x2 = 12.0625 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 12.0625 Calculate the square root of the right side: 3.473110997 Break this problem into two subproblems by setting (x + 3.25) equal to 3.473110997 and -3.473110997.Subproblem 1
x + 3.25 = 3.473110997 Simplifying x + 3.25 = 3.473110997 Reorder the terms: 3.25 + x = 3.473110997 Solving 3.25 + x = 3.473110997 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 = 3.473110997 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 3.473110997 + -3.25 x = 3.473110997 + -3.25 Combine like terms: 3.473110997 + -3.25 = 0.223110997 x = 0.223110997 Simplifying x = 0.223110997Subproblem 2
x + 3.25 = -3.473110997 Simplifying x + 3.25 = -3.473110997 Reorder the terms: 3.25 + x = -3.473110997 Solving 3.25 + x = -3.473110997 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 = -3.473110997 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -3.473110997 + -3.25 x = -3.473110997 + -3.25 Combine like terms: -3.473110997 + -3.25 = -6.723110997 x = -6.723110997 Simplifying x = -6.723110997Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.223110997, -6.723110997}
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