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Simplifying -0.667(x2 + -12x + 36) + 7 = 0 Reorder the terms: -0.667(36 + -12x + x2) + 7 = 0 (36 * -0.667 + -12x * -0.667 + x2 * -0.667) + 7 = 0 (-24.012 + 8.004x + -0.667x2) + 7 = 0 Reorder the terms: -24.012 + 7 + 8.004x + -0.667x2 = 0 Combine like terms: -24.012 + 7 = -17.012 -17.012 + 8.004x + -0.667x2 = 0 Solving -17.012 + 8.004x + -0.667x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.667 the coefficient of the squared term: Divide each side by '-0.667'. 25.50524738 + -12x + x2 = 0 Move the constant term to the right: Add '-25.50524738' to each side of the equation. 25.50524738 + -12x + -25.50524738 + x2 = 0 + -25.50524738 Reorder the terms: 25.50524738 + -25.50524738 + -12x + x2 = 0 + -25.50524738 Combine like terms: 25.50524738 + -25.50524738 = 0.00000000 0.00000000 + -12x + x2 = 0 + -25.50524738 -12x + x2 = 0 + -25.50524738 Combine like terms: 0 + -25.50524738 = -25.50524738 -12x + x2 = -25.50524738 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 = -25.50524738 + 36 Reorder the terms: 36 + -12x + x2 = -25.50524738 + 36 Combine like terms: -25.50524738 + 36 = 10.49475262 36 + -12x + x2 = 10.49475262 Factor a perfect square on the left side: (x + -6)(x + -6) = 10.49475262 Calculate the square root of the right side: 3.23956056 Break this problem into two subproblems by setting (x + -6) equal to 3.23956056 and -3.23956056.Subproblem 1
x + -6 = 3.23956056 Simplifying x + -6 = 3.23956056 Reorder the terms: -6 + x = 3.23956056 Solving -6 + x = 3.23956056 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 = 3.23956056 + 6 Combine like terms: -6 + 6 = 0 0 + x = 3.23956056 + 6 x = 3.23956056 + 6 Combine like terms: 3.23956056 + 6 = 9.23956056 x = 9.23956056 Simplifying x = 9.23956056Subproblem 2
x + -6 = -3.23956056 Simplifying x + -6 = -3.23956056 Reorder the terms: -6 + x = -3.23956056 Solving -6 + x = -3.23956056 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 = -3.23956056 + 6 Combine like terms: -6 + 6 = 0 0 + x = -3.23956056 + 6 x = -3.23956056 + 6 Combine like terms: -3.23956056 + 6 = 2.76043944 x = 2.76043944 Simplifying x = 2.76043944Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.23956056, 2.76043944}
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