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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 = 29 29 + -18x + 3x2 = 26 Solving 29 + -18x + 3x2 = 26 Solving for variable 'x'. Reorder the terms: 29 + -26 + -18x + 3x2 = 26 + -26 Combine like terms: 29 + -26 = 3 3 + -18x + 3x2 = 26 + -26 Combine like terms: 26 + -26 = 0 3 + -18x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(1 + -6x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -6x + x2)' equal to zero and attempt to solve: Simplifying 1 + -6x + x2 = 0 Solving 1 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -6x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -6x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6x + x2 = 0 + -1 -6x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -6x + x2 = -1 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 = -1 + 9 Reorder the terms: 9 + -6x + x2 = -1 + 9 Combine like terms: -1 + 9 = 8 9 + -6x + x2 = 8 Factor a perfect square on the left side: (x + -3)(x + -3) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (x + -3) equal to 2.828427125 and -2.828427125.Subproblem 1
x + -3 = 2.828427125 Simplifying x + -3 = 2.828427125 Reorder the terms: -3 + x = 2.828427125 Solving -3 + x = 2.828427125 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 = 2.828427125 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.828427125 + 3 x = 2.828427125 + 3 Combine like terms: 2.828427125 + 3 = 5.828427125 x = 5.828427125 Simplifying x = 5.828427125Subproblem 2
x + -3 = -2.828427125 Simplifying x + -3 = -2.828427125 Reorder the terms: -3 + x = -2.828427125 Solving -3 + x = -2.828427125 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 = -2.828427125 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.828427125 + 3 x = -2.828427125 + 3 Combine like terms: -2.828427125 + 3 = 0.171572875 x = 0.171572875 Simplifying x = 0.171572875Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.828427125, 0.171572875}Solution
x = {5.828427125, 0.171572875}
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