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Simplifying -3(x + -1)(x + -1) + 6 = -200 Reorder the terms: -3(-1 + x)(x + -1) + 6 = -200 Reorder the terms: -3(-1 + x)(-1 + x) + 6 = -200 Multiply (-1 + x) * (-1 + x) -3(-1(-1 + x) + x(-1 + x)) + 6 = -200 -3((-1 * -1 + x * -1) + x(-1 + x)) + 6 = -200 -3((1 + -1x) + x(-1 + x)) + 6 = -200 -3(1 + -1x + (-1 * x + x * x)) + 6 = -200 -3(1 + -1x + (-1x + x2)) + 6 = -200 Combine like terms: -1x + -1x = -2x -3(1 + -2x + x2) + 6 = -200 (1 * -3 + -2x * -3 + x2 * -3) + 6 = -200 (-3 + 6x + -3x2) + 6 = -200 Reorder the terms: -3 + 6 + 6x + -3x2 = -200 Combine like terms: -3 + 6 = 3 3 + 6x + -3x2 = -200 Solving 3 + 6x + -3x2 = -200 Solving for variable 'x'. Reorder the terms: 3 + 200 + 6x + -3x2 = -200 + 200 Combine like terms: 3 + 200 = 203 203 + 6x + -3x2 = -200 + 200 Combine like terms: -200 + 200 = 0 203 + 6x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -67.66666667 + -2x + x2 = 0 Move the constant term to the right: Add '67.66666667' to each side of the equation. -67.66666667 + -2x + 67.66666667 + x2 = 0 + 67.66666667 Reorder the terms: -67.66666667 + 67.66666667 + -2x + x2 = 0 + 67.66666667 Combine like terms: -67.66666667 + 67.66666667 = 0.00000000 0.00000000 + -2x + x2 = 0 + 67.66666667 -2x + x2 = 0 + 67.66666667 Combine like terms: 0 + 67.66666667 = 67.66666667 -2x + x2 = 67.66666667 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 67.66666667 + 1 Reorder the terms: 1 + -2x + x2 = 67.66666667 + 1 Combine like terms: 67.66666667 + 1 = 68.66666667 1 + -2x + x2 = 68.66666667 Factor a perfect square on the left side: (x + -1)(x + -1) = 68.66666667 Calculate the square root of the right side: 8.286535263 Break this problem into two subproblems by setting (x + -1) equal to 8.286535263 and -8.286535263.Subproblem 1
x + -1 = 8.286535263 Simplifying x + -1 = 8.286535263 Reorder the terms: -1 + x = 8.286535263 Solving -1 + x = 8.286535263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 8.286535263 + 1 Combine like terms: -1 + 1 = 0 0 + x = 8.286535263 + 1 x = 8.286535263 + 1 Combine like terms: 8.286535263 + 1 = 9.286535263 x = 9.286535263 Simplifying x = 9.286535263Subproblem 2
x + -1 = -8.286535263 Simplifying x + -1 = -8.286535263 Reorder the terms: -1 + x = -8.286535263 Solving -1 + x = -8.286535263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -8.286535263 + 1 Combine like terms: -1 + 1 = 0 0 + x = -8.286535263 + 1 x = -8.286535263 + 1 Combine like terms: -8.286535263 + 1 = -7.286535263 x = -7.286535263 Simplifying x = -7.286535263Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.286535263, -7.286535263}
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