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Simplifying x2 + -13.895x + -136.88 = 0 Reorder the terms: -136.88 + -13.895x + x2 = 0 Solving -136.88 + -13.895x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '136.88' to each side of the equation. -136.88 + -13.895x + 136.88 + x2 = 0 + 136.88 Reorder the terms: -136.88 + 136.88 + -13.895x + x2 = 0 + 136.88 Combine like terms: -136.88 + 136.88 = 0.00 0.00 + -13.895x + x2 = 0 + 136.88 -13.895x + x2 = 0 + 136.88 Combine like terms: 0 + 136.88 = 136.88 -13.895x + x2 = 136.88 The x term is -13.895x. Take half its coefficient (-6.9475). Square it (48.26775625) and add it to both sides. Add '48.26775625' to each side of the equation. -13.895x + 48.26775625 + x2 = 136.88 + 48.26775625 Reorder the terms: 48.26775625 + -13.895x + x2 = 136.88 + 48.26775625 Combine like terms: 136.88 + 48.26775625 = 185.14775625 48.26775625 + -13.895x + x2 = 185.14775625 Factor a perfect square on the left side: (x + -6.9475)(x + -6.9475) = 185.14775625 Calculate the square root of the right side: 13.606901052 Break this problem into two subproblems by setting (x + -6.9475) equal to 13.606901052 and -13.606901052.Subproblem 1
x + -6.9475 = 13.606901052 Simplifying x + -6.9475 = 13.606901052 Reorder the terms: -6.9475 + x = 13.606901052 Solving -6.9475 + x = 13.606901052 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.9475' to each side of the equation. -6.9475 + 6.9475 + x = 13.606901052 + 6.9475 Combine like terms: -6.9475 + 6.9475 = 0.0000 0.0000 + x = 13.606901052 + 6.9475 x = 13.606901052 + 6.9475 Combine like terms: 13.606901052 + 6.9475 = 20.554401052 x = 20.554401052 Simplifying x = 20.554401052Subproblem 2
x + -6.9475 = -13.606901052 Simplifying x + -6.9475 = -13.606901052 Reorder the terms: -6.9475 + x = -13.606901052 Solving -6.9475 + x = -13.606901052 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.9475' to each side of the equation. -6.9475 + 6.9475 + x = -13.606901052 + 6.9475 Combine like terms: -6.9475 + 6.9475 = 0.0000 0.0000 + x = -13.606901052 + 6.9475 x = -13.606901052 + 6.9475 Combine like terms: -13.606901052 + 6.9475 = -6.659401052 x = -6.659401052 Simplifying x = -6.659401052Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.554401052, -6.659401052}
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