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Simplifying (2x2) + 3x + -72 = 0 Reorder the terms: -72 + 3x + (2x2) = 0 Solving -72 + 3x + (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'. -36 + 1.5x + x2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + 1.5x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + 1.5x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 1.5x + x2 = 0 + 36 1.5x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 1.5x + x2 = 36 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 36 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 36 + 0.5625 Combine like terms: 36 + 0.5625 = 36.5625 0.5625 + 1.5x + x2 = 36.5625 Factor a perfect square on the left side: ((x) + 0.75)((x) + 0.75) = 36.5625 Calculate the square root of the right side: 6.046693311 Break this problem into two subproblems by setting ((x) + 0.75) equal to 6.046693311 and -6.046693311.Subproblem 1
(x) + 0.75 = 6.046693311 Simplifying (x) + 0.75 = 6.046693311 x + 0.75 = 6.046693311 Reorder the terms: 0.75 + x = 6.046693311 Solving 0.75 + x = 6.046693311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 6.046693311 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 6.046693311 + -0.75 x = 6.046693311 + -0.75 Combine like terms: 6.046693311 + -0.75 = 5.296693311 x = 5.296693311 Simplifying x = 5.296693311Subproblem 2
(x) + 0.75 = -6.046693311 Simplifying (x) + 0.75 = -6.046693311 x + 0.75 = -6.046693311 Reorder the terms: 0.75 + x = -6.046693311 Solving 0.75 + x = -6.046693311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -6.046693311 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -6.046693311 + -0.75 x = -6.046693311 + -0.75 Combine like terms: -6.046693311 + -0.75 = -6.796693311 x = -6.796693311 Simplifying x = -6.796693311Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.296693311, -6.796693311}
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