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Simplifying 3x(-1x + 7) = 23 + -3(x + 2) Reorder the terms: 3x(7 + -1x) = 23 + -3(x + 2) (7 * 3x + -1x * 3x) = 23 + -3(x + 2) (21x + -3x2) = 23 + -3(x + 2) Reorder the terms: 21x + -3x2 = 23 + -3(2 + x) 21x + -3x2 = 23 + (2 * -3 + x * -3) 21x + -3x2 = 23 + (-6 + -3x) Combine like terms: 23 + -6 = 17 21x + -3x2 = 17 + -3x Solving 21x + -3x2 = 17 + -3x Solving for variable 'x'. Reorder the terms: -17 + 21x + 3x + -3x2 = 17 + -3x + -17 + 3x Combine like terms: 21x + 3x = 24x -17 + 24x + -3x2 = 17 + -3x + -17 + 3x Reorder the terms: -17 + 24x + -3x2 = 17 + -17 + -3x + 3x Combine like terms: 17 + -17 = 0 -17 + 24x + -3x2 = 0 + -3x + 3x -17 + 24x + -3x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -17 + 24x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 5.666666667 + -8x + x2 = 0 Move the constant term to the right: Add '-5.666666667' to each side of the equation. 5.666666667 + -8x + -5.666666667 + x2 = 0 + -5.666666667 Reorder the terms: 5.666666667 + -5.666666667 + -8x + x2 = 0 + -5.666666667 Combine like terms: 5.666666667 + -5.666666667 = 0.000000000 0.000000000 + -8x + x2 = 0 + -5.666666667 -8x + x2 = 0 + -5.666666667 Combine like terms: 0 + -5.666666667 = -5.666666667 -8x + x2 = -5.666666667 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -5.666666667 + 16 Reorder the terms: 16 + -8x + x2 = -5.666666667 + 16 Combine like terms: -5.666666667 + 16 = 10.333333333 16 + -8x + x2 = 10.333333333 Factor a perfect square on the left side: (x + -4)(x + -4) = 10.333333333 Calculate the square root of the right side: 3.214550254 Break this problem into two subproblems by setting (x + -4) equal to 3.214550254 and -3.214550254.Subproblem 1
x + -4 = 3.214550254 Simplifying x + -4 = 3.214550254 Reorder the terms: -4 + x = 3.214550254 Solving -4 + x = 3.214550254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 3.214550254 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.214550254 + 4 x = 3.214550254 + 4 Combine like terms: 3.214550254 + 4 = 7.214550254 x = 7.214550254 Simplifying x = 7.214550254Subproblem 2
x + -4 = -3.214550254 Simplifying x + -4 = -3.214550254 Reorder the terms: -4 + x = -3.214550254 Solving -4 + x = -3.214550254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -3.214550254 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.214550254 + 4 x = -3.214550254 + 4 Combine like terms: -3.214550254 + 4 = 0.785449746 x = 0.785449746 Simplifying x = 0.785449746Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.214550254, 0.785449746}
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