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Simplifying 13 + -1x(5x + -11) = -13 Reorder the terms: 13 + -1x(-11 + 5x) = -13 13 + (-11 * -1x + 5x * -1x) = -13 13 + (11x + -5x2) = -13 Solving 13 + 11x + -5x2 = -13 Solving for variable 'x'. Reorder the terms: 13 + 13 + 11x + -5x2 = -13 + 13 Combine like terms: 13 + 13 = 26 26 + 11x + -5x2 = -13 + 13 Combine like terms: -13 + 13 = 0 26 + 11x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -5.2 + -2.2x + x2 = 0 Move the constant term to the right: Add '5.2' to each side of the equation. -5.2 + -2.2x + 5.2 + x2 = 0 + 5.2 Reorder the terms: -5.2 + 5.2 + -2.2x + x2 = 0 + 5.2 Combine like terms: -5.2 + 5.2 = 0.0 0.0 + -2.2x + x2 = 0 + 5.2 -2.2x + x2 = 0 + 5.2 Combine like terms: 0 + 5.2 = 5.2 -2.2x + x2 = 5.2 The x term is -2.2x. Take half its coefficient (-1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. -2.2x + 1.21 + x2 = 5.2 + 1.21 Reorder the terms: 1.21 + -2.2x + x2 = 5.2 + 1.21 Combine like terms: 5.2 + 1.21 = 6.41 1.21 + -2.2x + x2 = 6.41 Factor a perfect square on the left side: (x + -1.1)(x + -1.1) = 6.41 Calculate the square root of the right side: 2.53179778 Break this problem into two subproblems by setting (x + -1.1) equal to 2.53179778 and -2.53179778.Subproblem 1
x + -1.1 = 2.53179778 Simplifying x + -1.1 = 2.53179778 Reorder the terms: -1.1 + x = 2.53179778 Solving -1.1 + x = 2.53179778 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = 2.53179778 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = 2.53179778 + 1.1 x = 2.53179778 + 1.1 Combine like terms: 2.53179778 + 1.1 = 3.63179778 x = 3.63179778 Simplifying x = 3.63179778Subproblem 2
x + -1.1 = -2.53179778 Simplifying x + -1.1 = -2.53179778 Reorder the terms: -1.1 + x = -2.53179778 Solving -1.1 + x = -2.53179778 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = -2.53179778 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = -2.53179778 + 1.1 x = -2.53179778 + 1.1 Combine like terms: -2.53179778 + 1.1 = -1.43179778 x = -1.43179778 Simplifying x = -1.43179778Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.63179778, -1.43179778}
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