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Simplifying 2x2 + 3.4x + -2.89 = 0 Reorder the terms: -2.89 + 3.4x + 2x2 = 0 Solving -2.89 + 3.4x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.445 + 1.7x + x2 = 0 Move the constant term to the right: Add '1.445' to each side of the equation. -1.445 + 1.7x + 1.445 + x2 = 0 + 1.445 Reorder the terms: -1.445 + 1.445 + 1.7x + x2 = 0 + 1.445 Combine like terms: -1.445 + 1.445 = 0.000 0.000 + 1.7x + x2 = 0 + 1.445 1.7x + x2 = 0 + 1.445 Combine like terms: 0 + 1.445 = 1.445 1.7x + x2 = 1.445 The x term is 1.7x. Take half its coefficient (0.85). Square it (0.7225) and add it to both sides. Add '0.7225' to each side of the equation. 1.7x + 0.7225 + x2 = 1.445 + 0.7225 Reorder the terms: 0.7225 + 1.7x + x2 = 1.445 + 0.7225 Combine like terms: 1.445 + 0.7225 = 2.1675 0.7225 + 1.7x + x2 = 2.1675 Factor a perfect square on the left side: (x + 0.85)(x + 0.85) = 2.1675 Calculate the square root of the right side: 1.472243186 Break this problem into two subproblems by setting (x + 0.85) equal to 1.472243186 and -1.472243186.Subproblem 1
x + 0.85 = 1.472243186 Simplifying x + 0.85 = 1.472243186 Reorder the terms: 0.85 + x = 1.472243186 Solving 0.85 + x = 1.472243186 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.85' to each side of the equation. 0.85 + -0.85 + x = 1.472243186 + -0.85 Combine like terms: 0.85 + -0.85 = 0.00 0.00 + x = 1.472243186 + -0.85 x = 1.472243186 + -0.85 Combine like terms: 1.472243186 + -0.85 = 0.622243186 x = 0.622243186 Simplifying x = 0.622243186Subproblem 2
x + 0.85 = -1.472243186 Simplifying x + 0.85 = -1.472243186 Reorder the terms: 0.85 + x = -1.472243186 Solving 0.85 + x = -1.472243186 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.85' to each side of the equation. 0.85 + -0.85 + x = -1.472243186 + -0.85 Combine like terms: 0.85 + -0.85 = 0.00 0.00 + x = -1.472243186 + -0.85 x = -1.472243186 + -0.85 Combine like terms: -1.472243186 + -0.85 = -2.322243186 x = -2.322243186 Simplifying x = -2.322243186Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.622243186, -2.322243186}
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