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Simplifying 234x2 + -3556 + -1(344x + 445) = 346 Reorder the terms: 234x2 + -3556 + -1(445 + 344x) = 346 234x2 + -3556 + (445 * -1 + 344x * -1) = 346 234x2 + -3556 + (-445 + -344x) = 346 Reorder the terms: -3556 + -445 + -344x + 234x2 = 346 Combine like terms: -3556 + -445 = -4001 -4001 + -344x + 234x2 = 346 Solving -4001 + -344x + 234x2 = 346 Solving for variable 'x'. Reorder the terms: -4001 + -346 + -344x + 234x2 = 346 + -346 Combine like terms: -4001 + -346 = -4347 -4347 + -344x + 234x2 = 346 + -346 Combine like terms: 346 + -346 = 0 -4347 + -344x + 234x2 = 0 Begin completing the square. Divide all terms by 234 the coefficient of the squared term: Divide each side by '234'. -18.57692308 + -1.47008547x + x2 = 0 Move the constant term to the right: Add '18.57692308' to each side of the equation. -18.57692308 + -1.47008547x + 18.57692308 + x2 = 0 + 18.57692308 Reorder the terms: -18.57692308 + 18.57692308 + -1.47008547x + x2 = 0 + 18.57692308 Combine like terms: -18.57692308 + 18.57692308 = 0.00000000 0.00000000 + -1.47008547x + x2 = 0 + 18.57692308 -1.47008547x + x2 = 0 + 18.57692308 Combine like terms: 0 + 18.57692308 = 18.57692308 -1.47008547x + x2 = 18.57692308 The x term is -1.47008547x. Take half its coefficient (-0.735042735). Square it (0.5402878223) and add it to both sides. Add '0.5402878223' to each side of the equation. -1.47008547x + 0.5402878223 + x2 = 18.57692308 + 0.5402878223 Reorder the terms: 0.5402878223 + -1.47008547x + x2 = 18.57692308 + 0.5402878223 Combine like terms: 18.57692308 + 0.5402878223 = 19.1172109023 0.5402878223 + -1.47008547x + x2 = 19.1172109023 Factor a perfect square on the left side: (x + -0.735042735)(x + -0.735042735) = 19.1172109023 Calculate the square root of the right side: 4.372323284 Break this problem into two subproblems by setting (x + -0.735042735) equal to 4.372323284 and -4.372323284.Subproblem 1
x + -0.735042735 = 4.372323284 Simplifying x + -0.735042735 = 4.372323284 Reorder the terms: -0.735042735 + x = 4.372323284 Solving -0.735042735 + x = 4.372323284 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.735042735' to each side of the equation. -0.735042735 + 0.735042735 + x = 4.372323284 + 0.735042735 Combine like terms: -0.735042735 + 0.735042735 = 0.000000000 0.000000000 + x = 4.372323284 + 0.735042735 x = 4.372323284 + 0.735042735 Combine like terms: 4.372323284 + 0.735042735 = 5.107366019 x = 5.107366019 Simplifying x = 5.107366019Subproblem 2
x + -0.735042735 = -4.372323284 Simplifying x + -0.735042735 = -4.372323284 Reorder the terms: -0.735042735 + x = -4.372323284 Solving -0.735042735 + x = -4.372323284 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.735042735' to each side of the equation. -0.735042735 + 0.735042735 + x = -4.372323284 + 0.735042735 Combine like terms: -0.735042735 + 0.735042735 = 0.000000000 0.000000000 + x = -4.372323284 + 0.735042735 x = -4.372323284 + 0.735042735 Combine like terms: -4.372323284 + 0.735042735 = -3.637280549 x = -3.637280549 Simplifying x = -3.637280549Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.107366019, -3.637280549}
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