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Simplifying 2.3x2 + -1.9x = 6.8 Reorder the terms: -1.9x + 2.3x2 = 6.8 Solving -1.9x + 2.3x2 = 6.8 Solving for variable 'x'. Reorder the terms: -6.8 + -1.9x + 2.3x2 = 6.8 + -6.8 Combine like terms: 6.8 + -6.8 = 0.0 -6.8 + -1.9x + 2.3x2 = 0.0 Begin completing the square. Divide all terms by 2.3 the coefficient of the squared term: Divide each side by '2.3'. -2.956521739 + -0.8260869565x + x2 = 0 Move the constant term to the right: Add '2.956521739' to each side of the equation. -2.956521739 + -0.8260869565x + 2.956521739 + x2 = 0 + 2.956521739 Reorder the terms: -2.956521739 + 2.956521739 + -0.8260869565x + x2 = 0 + 2.956521739 Combine like terms: -2.956521739 + 2.956521739 = 0.000000000 0.000000000 + -0.8260869565x + x2 = 0 + 2.956521739 -0.8260869565x + x2 = 0 + 2.956521739 Combine like terms: 0 + 2.956521739 = 2.956521739 -0.8260869565x + x2 = 2.956521739 The x term is -0.8260869565x. Take half its coefficient (-0.4130434783). Square it (0.1706049150) and add it to both sides. Add '0.1706049150' to each side of the equation. -0.8260869565x + 0.1706049150 + x2 = 2.956521739 + 0.1706049150 Reorder the terms: 0.1706049150 + -0.8260869565x + x2 = 2.956521739 + 0.1706049150 Combine like terms: 2.956521739 + 0.1706049150 = 3.127126654 0.1706049150 + -0.8260869565x + x2 = 3.127126654 Factor a perfect square on the left side: (x + -0.4130434783)(x + -0.4130434783) = 3.127126654 Calculate the square root of the right side: 1.768368359 Break this problem into two subproblems by setting (x + -0.4130434783) equal to 1.768368359 and -1.768368359.Subproblem 1
x + -0.4130434783 = 1.768368359 Simplifying x + -0.4130434783 = 1.768368359 Reorder the terms: -0.4130434783 + x = 1.768368359 Solving -0.4130434783 + x = 1.768368359 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4130434783' to each side of the equation. -0.4130434783 + 0.4130434783 + x = 1.768368359 + 0.4130434783 Combine like terms: -0.4130434783 + 0.4130434783 = 0.0000000000 0.0000000000 + x = 1.768368359 + 0.4130434783 x = 1.768368359 + 0.4130434783 Combine like terms: 1.768368359 + 0.4130434783 = 2.1814118373 x = 2.1814118373 Simplifying x = 2.1814118373Subproblem 2
x + -0.4130434783 = -1.768368359 Simplifying x + -0.4130434783 = -1.768368359 Reorder the terms: -0.4130434783 + x = -1.768368359 Solving -0.4130434783 + x = -1.768368359 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4130434783' to each side of the equation. -0.4130434783 + 0.4130434783 + x = -1.768368359 + 0.4130434783 Combine like terms: -0.4130434783 + 0.4130434783 = 0.0000000000 0.0000000000 + x = -1.768368359 + 0.4130434783 x = -1.768368359 + 0.4130434783 Combine like terms: -1.768368359 + 0.4130434783 = -1.3553248807 x = -1.3553248807 Simplifying x = -1.3553248807Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1814118373, -1.3553248807}
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