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Simplifying x2 + -12x + -84 = 0 Reorder the terms: -84 + -12x + x2 = 0 Solving -84 + -12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '84' to each side of the equation. -84 + -12x + 84 + x2 = 0 + 84 Reorder the terms: -84 + 84 + -12x + x2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + -12x + x2 = 0 + 84 -12x + x2 = 0 + 84 Combine like terms: 0 + 84 = 84 -12x + x2 = 84 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 = 84 + 36 Reorder the terms: 36 + -12x + x2 = 84 + 36 Combine like terms: 84 + 36 = 120 36 + -12x + x2 = 120 Factor a perfect square on the left side: (x + -6)(x + -6) = 120 Calculate the square root of the right side: 10.95445115 Break this problem into two subproblems by setting (x + -6) equal to 10.95445115 and -10.95445115.Subproblem 1
x + -6 = 10.95445115 Simplifying x + -6 = 10.95445115 Reorder the terms: -6 + x = 10.95445115 Solving -6 + x = 10.95445115 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 = 10.95445115 + 6 Combine like terms: -6 + 6 = 0 0 + x = 10.95445115 + 6 x = 10.95445115 + 6 Combine like terms: 10.95445115 + 6 = 16.95445115 x = 16.95445115 Simplifying x = 16.95445115Subproblem 2
x + -6 = -10.95445115 Simplifying x + -6 = -10.95445115 Reorder the terms: -6 + x = -10.95445115 Solving -6 + x = -10.95445115 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 = -10.95445115 + 6 Combine like terms: -6 + 6 = 0 0 + x = -10.95445115 + 6 x = -10.95445115 + 6 Combine like terms: -10.95445115 + 6 = -4.95445115 x = -4.95445115 Simplifying x = -4.95445115Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.95445115, -4.95445115}
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