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Simplifying 2x2 + 3x + -60 = 0 Reorder the terms: -60 + 3x + 2x2 = 0 Solving -60 + 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'. -30 + 1.5x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + 1.5x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 1.5x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 1.5x + x2 = 0 + 30 1.5x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 1.5x + x2 = 30 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 = 30 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 30 + 0.5625 Combine like terms: 30 + 0.5625 = 30.5625 0.5625 + 1.5x + x2 = 30.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 30.5625 Calculate the square root of the right side: 5.528336097 Break this problem into two subproblems by setting (x + 0.75) equal to 5.528336097 and -5.528336097.Subproblem 1
x + 0.75 = 5.528336097 Simplifying x + 0.75 = 5.528336097 Reorder the terms: 0.75 + x = 5.528336097 Solving 0.75 + x = 5.528336097 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 = 5.528336097 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 5.528336097 + -0.75 x = 5.528336097 + -0.75 Combine like terms: 5.528336097 + -0.75 = 4.778336097 x = 4.778336097 Simplifying x = 4.778336097Subproblem 2
x + 0.75 = -5.528336097 Simplifying x + 0.75 = -5.528336097 Reorder the terms: 0.75 + x = -5.528336097 Solving 0.75 + x = -5.528336097 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 = -5.528336097 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -5.528336097 + -0.75 x = -5.528336097 + -0.75 Combine like terms: -5.528336097 + -0.75 = -6.278336097 x = -6.278336097 Simplifying x = -6.278336097Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.778336097, -6.278336097}
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