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Simplifying 3x + 20 = 4 + -3x(8 + -3x) Reorder the terms: 20 + 3x = 4 + -3x(8 + -3x) 20 + 3x = 4 + (8 * -3x + -3x * -3x) 20 + 3x = 4 + (-24x + 9x2) Solving 20 + 3x = 4 + -24x + 9x2 Solving for variable 'x'. Reorder the terms: 20 + -4 + 3x + 24x + -9x2 = 4 + -24x + 9x2 + -4 + 24x + -9x2 Combine like terms: 20 + -4 = 16 16 + 3x + 24x + -9x2 = 4 + -24x + 9x2 + -4 + 24x + -9x2 Combine like terms: 3x + 24x = 27x 16 + 27x + -9x2 = 4 + -24x + 9x2 + -4 + 24x + -9x2 Reorder the terms: 16 + 27x + -9x2 = 4 + -4 + -24x + 24x + 9x2 + -9x2 Combine like terms: 4 + -4 = 0 16 + 27x + -9x2 = 0 + -24x + 24x + 9x2 + -9x2 16 + 27x + -9x2 = -24x + 24x + 9x2 + -9x2 Combine like terms: -24x + 24x = 0 16 + 27x + -9x2 = 0 + 9x2 + -9x2 16 + 27x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 16 + 27x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -1.777777778 + -3x + x2 = 0 Move the constant term to the right: Add '1.777777778' to each side of the equation. -1.777777778 + -3x + 1.777777778 + x2 = 0 + 1.777777778 Reorder the terms: -1.777777778 + 1.777777778 + -3x + x2 = 0 + 1.777777778 Combine like terms: -1.777777778 + 1.777777778 = 0.000000000 0.000000000 + -3x + x2 = 0 + 1.777777778 -3x + x2 = 0 + 1.777777778 Combine like terms: 0 + 1.777777778 = 1.777777778 -3x + x2 = 1.777777778 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 1.777777778 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 1.777777778 + 2.25 Combine like terms: 1.777777778 + 2.25 = 4.027777778 2.25 + -3x + x2 = 4.027777778 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 4.027777778 Calculate the square root of the right side: 2.00693243 Break this problem into two subproblems by setting (x + -1.5) equal to 2.00693243 and -2.00693243.Subproblem 1
x + -1.5 = 2.00693243 Simplifying x + -1.5 = 2.00693243 Reorder the terms: -1.5 + x = 2.00693243 Solving -1.5 + x = 2.00693243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 2.00693243 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.00693243 + 1.5 x = 2.00693243 + 1.5 Combine like terms: 2.00693243 + 1.5 = 3.50693243 x = 3.50693243 Simplifying x = 3.50693243Subproblem 2
x + -1.5 = -2.00693243 Simplifying x + -1.5 = -2.00693243 Reorder the terms: -1.5 + x = -2.00693243 Solving -1.5 + x = -2.00693243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -2.00693243 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.00693243 + 1.5 x = -2.00693243 + 1.5 Combine like terms: -2.00693243 + 1.5 = -0.50693243 x = -0.50693243 Simplifying x = -0.50693243Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.50693243, -0.50693243}
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