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Simplifying 0 = x2 + -12x + 12 Reorder the terms: 0 = 12 + -12x + x2 Solving 0 = 12 + -12x + x2 Solving for variable 'x'. Combine like terms: 0 + -12 = -12 -12 + 12x + -1x2 = 12 + -12x + x2 + -12 + 12x + -1x2 Reorder the terms: -12 + 12x + -1x2 = 12 + -12 + -12x + 12x + x2 + -1x2 Combine like terms: 12 + -12 = 0 -12 + 12x + -1x2 = 0 + -12x + 12x + x2 + -1x2 -12 + 12x + -1x2 = -12x + 12x + x2 + -1x2 Combine like terms: -12x + 12x = 0 -12 + 12x + -1x2 = 0 + x2 + -1x2 -12 + 12x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -12 + 12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 12 + -12x + x2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + -12x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -12x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -12x + x2 = 0 + -12 -12x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -12x + x2 = -12 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 = -12 + 36 Reorder the terms: 36 + -12x + x2 = -12 + 36 Combine like terms: -12 + 36 = 24 36 + -12x + x2 = 24 Factor a perfect square on the left side: (x + -6)(x + -6) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (x + -6) equal to 4.898979486 and -4.898979486.Subproblem 1
x + -6 = 4.898979486 Simplifying x + -6 = 4.898979486 Reorder the terms: -6 + x = 4.898979486 Solving -6 + x = 4.898979486 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 = 4.898979486 + 6 Combine like terms: -6 + 6 = 0 0 + x = 4.898979486 + 6 x = 4.898979486 + 6 Combine like terms: 4.898979486 + 6 = 10.898979486 x = 10.898979486 Simplifying x = 10.898979486Subproblem 2
x + -6 = -4.898979486 Simplifying x + -6 = -4.898979486 Reorder the terms: -6 + x = -4.898979486 Solving -6 + x = -4.898979486 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 = -4.898979486 + 6 Combine like terms: -6 + 6 = 0 0 + x = -4.898979486 + 6 x = -4.898979486 + 6 Combine like terms: -4.898979486 + 6 = 1.101020514 x = 1.101020514 Simplifying x = 1.101020514Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.898979486, 1.101020514}
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