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Simplifying x2 + -12x = -28 Reorder the terms: -12x + x2 = -28 Solving -12x + x2 = -28 Solving for variable 'x'. Reorder the terms: 28 + -12x + x2 = -28 + 28 Combine like terms: -28 + 28 = 0 28 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-28' to each side of the equation. 28 + -12x + -28 + x2 = 0 + -28 Reorder the terms: 28 + -28 + -12x + x2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + -12x + x2 = 0 + -28 -12x + x2 = 0 + -28 Combine like terms: 0 + -28 = -28 -12x + x2 = -28 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 = -28 + 36 Reorder the terms: 36 + -12x + x2 = -28 + 36 Combine like terms: -28 + 36 = 8 36 + -12x + x2 = 8 Factor a perfect square on the left side: (x + -6)(x + -6) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (x + -6) equal to 2.828427125 and -2.828427125.Subproblem 1
x + -6 = 2.828427125 Simplifying x + -6 = 2.828427125 Reorder the terms: -6 + x = 2.828427125 Solving -6 + x = 2.828427125 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 = 2.828427125 + 6 Combine like terms: -6 + 6 = 0 0 + x = 2.828427125 + 6 x = 2.828427125 + 6 Combine like terms: 2.828427125 + 6 = 8.828427125 x = 8.828427125 Simplifying x = 8.828427125Subproblem 2
x + -6 = -2.828427125 Simplifying x + -6 = -2.828427125 Reorder the terms: -6 + x = -2.828427125 Solving -6 + x = -2.828427125 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 = -2.828427125 + 6 Combine like terms: -6 + 6 = 0 0 + x = -2.828427125 + 6 x = -2.828427125 + 6 Combine like terms: -2.828427125 + 6 = 3.171572875 x = 3.171572875 Simplifying x = 3.171572875Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.828427125, 3.171572875}
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