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Simplifying 3(x + -3)(x + -3) + -2 = 26 Reorder the terms: 3(-3 + x)(x + -3) + -2 = 26 Reorder the terms: 3(-3 + x)(-3 + x) + -2 = 26 Multiply (-3 + x) * (-3 + x) 3(-3(-3 + x) + x(-3 + x)) + -2 = 26 3((-3 * -3 + x * -3) + x(-3 + x)) + -2 = 26 3((9 + -3x) + x(-3 + x)) + -2 = 26 3(9 + -3x + (-3 * x + x * x)) + -2 = 26 3(9 + -3x + (-3x + x2)) + -2 = 26 Combine like terms: -3x + -3x = -6x 3(9 + -6x + x2) + -2 = 26 (9 * 3 + -6x * 3 + x2 * 3) + -2 = 26 (27 + -18x + 3x2) + -2 = 26 Reorder the terms: 27 + -2 + -18x + 3x2 = 26 Combine like terms: 27 + -2 = 25 25 + -18x + 3x2 = 26 Solving 25 + -18x + 3x2 = 26 Solving for variable 'x'. Reorder the terms: 25 + -26 + -18x + 3x2 = 26 + -26 Combine like terms: 25 + -26 = -1 -1 + -18x + 3x2 = 26 + -26 Combine like terms: 26 + -26 = 0 -1 + -18x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.3333333333 + -6x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -6x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -6x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -6x + x2 = 0 + 0.3333333333 -6x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -6x + x2 = 0.3333333333 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 0.3333333333 + 9 Reorder the terms: 9 + -6x + x2 = 0.3333333333 + 9 Combine like terms: 0.3333333333 + 9 = 9.3333333333 9 + -6x + x2 = 9.3333333333 Factor a perfect square on the left side: (x + -3)(x + -3) = 9.3333333333 Calculate the square root of the right side: 3.055050463 Break this problem into two subproblems by setting (x + -3) equal to 3.055050463 and -3.055050463.Subproblem 1
x + -3 = 3.055050463 Simplifying x + -3 = 3.055050463 Reorder the terms: -3 + x = 3.055050463 Solving -3 + x = 3.055050463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.055050463 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.055050463 + 3 x = 3.055050463 + 3 Combine like terms: 3.055050463 + 3 = 6.055050463 x = 6.055050463 Simplifying x = 6.055050463Subproblem 2
x + -3 = -3.055050463 Simplifying x + -3 = -3.055050463 Reorder the terms: -3 + x = -3.055050463 Solving -3 + x = -3.055050463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.055050463 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.055050463 + 3 x = -3.055050463 + 3 Combine like terms: -3.055050463 + 3 = -0.055050463 x = -0.055050463 Simplifying x = -0.055050463Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.055050463, -0.055050463}
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