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Simplifying x2 + -12x2 + x + 30 = 0 Reorder the terms: 30 + x + x2 + -12x2 = 0 Combine like terms: x2 + -12x2 = -11x2 30 + x + -11x2 = 0 Solving 30 + x + -11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -11 the coefficient of the squared term: Divide each side by '-11'. -2.727272727 + -0.09090909091x + x2 = 0 Move the constant term to the right: Add '2.727272727' to each side of the equation. -2.727272727 + -0.09090909091x + 2.727272727 + x2 = 0 + 2.727272727 Reorder the terms: -2.727272727 + 2.727272727 + -0.09090909091x + x2 = 0 + 2.727272727 Combine like terms: -2.727272727 + 2.727272727 = 0.000000000 0.000000000 + -0.09090909091x + x2 = 0 + 2.727272727 -0.09090909091x + x2 = 0 + 2.727272727 Combine like terms: 0 + 2.727272727 = 2.727272727 -0.09090909091x + x2 = 2.727272727 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.09090909091x + 0.25 + x2 = 2.727272727 + 0.25 Reorder the terms: 0.25 + -0.09090909091x + x2 = 2.727272727 + 0.25 Combine like terms: 2.727272727 + 0.25 = 2.977272727 0.25 + -0.09090909091x + x2 = 2.977272727 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.977272727 Calculate the square root of the right side: 1.725477536 Break this problem into two subproblems by setting (x + 0.5) equal to 1.725477536 and -1.725477536.Subproblem 1
x + 0.5 = 1.725477536 Simplifying x + 0.5 = 1.725477536 Reorder the terms: 0.5 + x = 1.725477536 Solving 0.5 + x = 1.725477536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.725477536 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.725477536 + -0.5 x = 1.725477536 + -0.5 Combine like terms: 1.725477536 + -0.5 = 1.225477536 x = 1.225477536 Simplifying x = 1.225477536Subproblem 2
x + 0.5 = -1.725477536 Simplifying x + 0.5 = -1.725477536 Reorder the terms: 0.5 + x = -1.725477536 Solving 0.5 + x = -1.725477536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.725477536 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.725477536 + -0.5 x = -1.725477536 + -0.5 Combine like terms: -1.725477536 + -0.5 = -2.225477536 x = -2.225477536 Simplifying x = -2.225477536Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.225477536, -2.225477536}
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