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Simplifying 2x2 + -50 = 3x + 10 Reorder the terms: -50 + 2x2 = 3x + 10 Reorder the terms: -50 + 2x2 = 10 + 3x Solving -50 + 2x2 = 10 + 3x Solving for variable 'x'. Reorder the terms: -50 + -10 + -3x + 2x2 = 10 + 3x + -10 + -3x Combine like terms: -50 + -10 = -60 -60 + -3x + 2x2 = 10 + 3x + -10 + -3x Reorder the terms: -60 + -3x + 2x2 = 10 + -10 + 3x + -3x Combine like terms: 10 + -10 = 0 -60 + -3x + 2x2 = 0 + 3x + -3x -60 + -3x + 2x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -60 + -3x + 2x2 = 0 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 = 6.278336097 x = 6.278336097 Simplifying x = 6.278336097Subproblem 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 = -4.778336097 x = -4.778336097 Simplifying x = -4.778336097Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.278336097, -4.778336097}
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