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Simplifying x2 + -12x + -30 = -5 Reorder the terms: -30 + -12x + x2 = -5 Solving -30 + -12x + x2 = -5 Solving for variable 'x'. Reorder the terms: -30 + 5 + -12x + x2 = -5 + 5 Combine like terms: -30 + 5 = -25 -25 + -12x + x2 = -5 + 5 Combine like terms: -5 + 5 = 0 -25 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + -12x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + -12x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -12x + x2 = 0 + 25 -12x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 -12x + x2 = 25 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 25 + 36 Reorder the terms: 36 + -12x + x2 = 25 + 36 Combine like terms: 25 + 36 = 61 36 + -12x + x2 = 61 Factor a perfect square on the left side: (x + -6)(x + -6) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (x + -6) equal to 7.810249676 and -7.810249676.Subproblem 1
x + -6 = 7.810249676 Simplifying x + -6 = 7.810249676 Reorder the terms: -6 + x = 7.810249676 Solving -6 + x = 7.810249676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 7.810249676 + 6 Combine like terms: -6 + 6 = 0 0 + x = 7.810249676 + 6 x = 7.810249676 + 6 Combine like terms: 7.810249676 + 6 = 13.810249676 x = 13.810249676 Simplifying x = 13.810249676Subproblem 2
x + -6 = -7.810249676 Simplifying x + -6 = -7.810249676 Reorder the terms: -6 + x = -7.810249676 Solving -6 + x = -7.810249676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -7.810249676 + 6 Combine like terms: -6 + 6 = 0 0 + x = -7.810249676 + 6 x = -7.810249676 + 6 Combine like terms: -7.810249676 + 6 = -1.810249676 x = -1.810249676 Simplifying x = -1.810249676Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.810249676, -1.810249676}
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