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Simplifying 2x(2x + -3.4) = 8x + -6.8 Reorder the terms: 2x(-3.4 + 2x) = 8x + -6.8 (-3.4 * 2x + 2x * 2x) = 8x + -6.8 (-6.8x + 4x2) = 8x + -6.8 Reorder the terms: -6.8x + 4x2 = -6.8 + 8x Solving -6.8x + 4x2 = -6.8 + 8x Solving for variable 'x'. Reorder the terms: 6.8 + -6.8x + -8x + 4x2 = -6.8 + 8x + 6.8 + -8x Combine like terms: -6.8x + -8x = -14.8x 6.8 + -14.8x + 4x2 = -6.8 + 8x + 6.8 + -8x Reorder the terms: 6.8 + -14.8x + 4x2 = -6.8 + 6.8 + 8x + -8x Combine like terms: -6.8 + 6.8 = 0.0 6.8 + -14.8x + 4x2 = 0.0 + 8x + -8x 6.8 + -14.8x + 4x2 = 8x + -8x Combine like terms: 8x + -8x = 0 6.8 + -14.8x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.7 + -3.7x + x2 = 0 Move the constant term to the right: Add '-1.7' to each side of the equation. 1.7 + -3.7x + -1.7 + x2 = 0 + -1.7 Reorder the terms: 1.7 + -1.7 + -3.7x + x2 = 0 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + -3.7x + x2 = 0 + -1.7 -3.7x + x2 = 0 + -1.7 Combine like terms: 0 + -1.7 = -1.7 -3.7x + x2 = -1.7 The x term is -3.7x. Take half its coefficient (-1.85). Square it (3.4225) and add it to both sides. Add '3.4225' to each side of the equation. -3.7x + 3.4225 + x2 = -1.7 + 3.4225 Reorder the terms: 3.4225 + -3.7x + x2 = -1.7 + 3.4225 Combine like terms: -1.7 + 3.4225 = 1.7225 3.4225 + -3.7x + x2 = 1.7225 Factor a perfect square on the left side: (x + -1.85)(x + -1.85) = 1.7225 Calculate the square root of the right side: 1.312440475 Break this problem into two subproblems by setting (x + -1.85) equal to 1.312440475 and -1.312440475.Subproblem 1
x + -1.85 = 1.312440475 Simplifying x + -1.85 = 1.312440475 Reorder the terms: -1.85 + x = 1.312440475 Solving -1.85 + x = 1.312440475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.85' to each side of the equation. -1.85 + 1.85 + x = 1.312440475 + 1.85 Combine like terms: -1.85 + 1.85 = 0.00 0.00 + x = 1.312440475 + 1.85 x = 1.312440475 + 1.85 Combine like terms: 1.312440475 + 1.85 = 3.162440475 x = 3.162440475 Simplifying x = 3.162440475Subproblem 2
x + -1.85 = -1.312440475 Simplifying x + -1.85 = -1.312440475 Reorder the terms: -1.85 + x = -1.312440475 Solving -1.85 + x = -1.312440475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.85' to each side of the equation. -1.85 + 1.85 + x = -1.312440475 + 1.85 Combine like terms: -1.85 + 1.85 = 0.00 0.00 + x = -1.312440475 + 1.85 x = -1.312440475 + 1.85 Combine like terms: -1.312440475 + 1.85 = 0.537559525 x = 0.537559525 Simplifying x = 0.537559525Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.162440475, 0.537559525}
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