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Simplifying 3x2 + -6x + 5 = 2x(4 + -1x) Reorder the terms: 5 + -6x + 3x2 = 2x(4 + -1x) 5 + -6x + 3x2 = (4 * 2x + -1x * 2x) 5 + -6x + 3x2 = (8x + -2x2) Solving 5 + -6x + 3x2 = 8x + -2x2 Solving for variable 'x'. Reorder the terms: 5 + -6x + -8x + 3x2 + 2x2 = 8x + -2x2 + -8x + 2x2 Combine like terms: -6x + -8x = -14x 5 + -14x + 3x2 + 2x2 = 8x + -2x2 + -8x + 2x2 Combine like terms: 3x2 + 2x2 = 5x2 5 + -14x + 5x2 = 8x + -2x2 + -8x + 2x2 Reorder the terms: 5 + -14x + 5x2 = 8x + -8x + -2x2 + 2x2 Combine like terms: 8x + -8x = 0 5 + -14x + 5x2 = 0 + -2x2 + 2x2 5 + -14x + 5x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 5 + -14x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1 + -2.8x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -2.8x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -2.8x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2.8x + x2 = 0 + -1 -2.8x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2.8x + x2 = -1 The x term is -2.8x. Take half its coefficient (-1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. -2.8x + 1.96 + x2 = -1 + 1.96 Reorder the terms: 1.96 + -2.8x + x2 = -1 + 1.96 Combine like terms: -1 + 1.96 = 0.96 1.96 + -2.8x + x2 = 0.96 Factor a perfect square on the left side: (x + -1.4)(x + -1.4) = 0.96 Calculate the square root of the right side: 0.979795897 Break this problem into two subproblems by setting (x + -1.4) equal to 0.979795897 and -0.979795897.Subproblem 1
x + -1.4 = 0.979795897 Simplifying x + -1.4 = 0.979795897 Reorder the terms: -1.4 + x = 0.979795897 Solving -1.4 + x = 0.979795897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = 0.979795897 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = 0.979795897 + 1.4 x = 0.979795897 + 1.4 Combine like terms: 0.979795897 + 1.4 = 2.379795897 x = 2.379795897 Simplifying x = 2.379795897Subproblem 2
x + -1.4 = -0.979795897 Simplifying x + -1.4 = -0.979795897 Reorder the terms: -1.4 + x = -0.979795897 Solving -1.4 + x = -0.979795897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = -0.979795897 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = -0.979795897 + 1.4 x = -0.979795897 + 1.4 Combine like terms: -0.979795897 + 1.4 = 0.420204103 x = 0.420204103 Simplifying x = 0.420204103Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.379795897, 0.420204103}
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