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Simplifying 3(2x + -14) * x = 15 + -1(-9x + -5) Reorder the terms: 3(-14 + 2x) * x = 15 + -1(-9x + -5) Reorder the terms for easier multiplication: 3x(-14 + 2x) = 15 + -1(-9x + -5) (-14 * 3x + 2x * 3x) = 15 + -1(-9x + -5) (-42x + 6x2) = 15 + -1(-9x + -5) Reorder the terms: -42x + 6x2 = 15 + -1(-5 + -9x) -42x + 6x2 = 15 + (-5 * -1 + -9x * -1) -42x + 6x2 = 15 + (5 + 9x) Combine like terms: 15 + 5 = 20 -42x + 6x2 = 20 + 9x Solving -42x + 6x2 = 20 + 9x Solving for variable 'x'. Reorder the terms: -20 + -42x + -9x + 6x2 = 20 + 9x + -20 + -9x Combine like terms: -42x + -9x = -51x -20 + -51x + 6x2 = 20 + 9x + -20 + -9x Reorder the terms: -20 + -51x + 6x2 = 20 + -20 + 9x + -9x Combine like terms: 20 + -20 = 0 -20 + -51x + 6x2 = 0 + 9x + -9x -20 + -51x + 6x2 = 9x + -9x Combine like terms: 9x + -9x = 0 -20 + -51x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -3.333333333 + -8.5x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + -8.5x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + -8.5x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + -8.5x + x2 = 0 + 3.333333333 -8.5x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 -8.5x + x2 = 3.333333333 The x term is -8.5x. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5x + 18.0625 + x2 = 3.333333333 + 18.0625 Reorder the terms: 18.0625 + -8.5x + x2 = 3.333333333 + 18.0625 Combine like terms: 3.333333333 + 18.0625 = 21.395833333 18.0625 + -8.5x + x2 = 21.395833333 Factor a perfect square on the left side: (x + -4.25)(x + -4.25) = 21.395833333 Calculate the square root of the right side: 4.625563029 Break this problem into two subproblems by setting (x + -4.25) equal to 4.625563029 and -4.625563029.Subproblem 1
x + -4.25 = 4.625563029 Simplifying x + -4.25 = 4.625563029 Reorder the terms: -4.25 + x = 4.625563029 Solving -4.25 + x = 4.625563029 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = 4.625563029 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = 4.625563029 + 4.25 x = 4.625563029 + 4.25 Combine like terms: 4.625563029 + 4.25 = 8.875563029 x = 8.875563029 Simplifying x = 8.875563029Subproblem 2
x + -4.25 = -4.625563029 Simplifying x + -4.25 = -4.625563029 Reorder the terms: -4.25 + x = -4.625563029 Solving -4.25 + x = -4.625563029 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = -4.625563029 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = -4.625563029 + 4.25 x = -4.625563029 + 4.25 Combine like terms: -4.625563029 + 4.25 = -0.375563029 x = -0.375563029 Simplifying x = -0.375563029Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.875563029, -0.375563029}
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