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Simplifying (3x + -4x2) + -1(6 + -5x2) = 0 Remove parenthesis around (3x + -4x2) 3x + -4x2 + -1(6 + -5x2) = 0 3x + -4x2 + (6 * -1 + -5x2 * -1) = 0 3x + -4x2 + (-6 + 5x2) = 0 Reorder the terms: -6 + 3x + -4x2 + 5x2 = 0 Combine like terms: -4x2 + 5x2 = 1x2 -6 + 3x + 1x2 = 0 Solving -6 + 3x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 3x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 3x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 3x + x2 = 0 + 6 3x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 3x + x2 = 6 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 6 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 6 + 2.25 Combine like terms: 6 + 2.25 = 8.25 2.25 + 3x + x2 = 8.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (x + 1.5) equal to 2.872281323 and -2.872281323.Subproblem 1
x + 1.5 = 2.872281323 Simplifying x + 1.5 = 2.872281323 Reorder the terms: 1.5 + x = 2.872281323 Solving 1.5 + x = 2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 2.872281323 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.872281323 + -1.5 x = 2.872281323 + -1.5 Combine like terms: 2.872281323 + -1.5 = 1.372281323 x = 1.372281323 Simplifying x = 1.372281323Subproblem 2
x + 1.5 = -2.872281323 Simplifying x + 1.5 = -2.872281323 Reorder the terms: 1.5 + x = -2.872281323 Solving 1.5 + x = -2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -2.872281323 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.872281323 + -1.5 x = -2.872281323 + -1.5 Combine like terms: -2.872281323 + -1.5 = -4.372281323 x = -4.372281323 Simplifying x = -4.372281323Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.372281323, -4.372281323}
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