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Simplifying 2(x * x) + 19x + -16 = 0 Multiply x * x 2(x2) + 19x + -16 = 0 Reorder the terms: -16 + 19x + 2x2 = 0 Solving -16 + 19x + 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'. -8 + 9.5x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 9.5x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 9.5x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 9.5x + x2 = 0 + 8 9.5x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 9.5x + x2 = 8 The x term is 9.5x. Take half its coefficient (4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. 9.5x + 22.5625 + x2 = 8 + 22.5625 Reorder the terms: 22.5625 + 9.5x + x2 = 8 + 22.5625 Combine like terms: 8 + 22.5625 = 30.5625 22.5625 + 9.5x + x2 = 30.5625 Factor a perfect square on the left side: (x + 4.75)(x + 4.75) = 30.5625 Calculate the square root of the right side: 5.528336097 Break this problem into two subproblems by setting (x + 4.75) equal to 5.528336097 and -5.528336097.Subproblem 1
x + 4.75 = 5.528336097 Simplifying x + 4.75 = 5.528336097 Reorder the terms: 4.75 + x = 5.528336097 Solving 4.75 + x = 5.528336097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = 5.528336097 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = 5.528336097 + -4.75 x = 5.528336097 + -4.75 Combine like terms: 5.528336097 + -4.75 = 0.778336097 x = 0.778336097 Simplifying x = 0.778336097Subproblem 2
x + 4.75 = -5.528336097 Simplifying x + 4.75 = -5.528336097 Reorder the terms: 4.75 + x = -5.528336097 Solving 4.75 + x = -5.528336097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = -5.528336097 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = -5.528336097 + -4.75 x = -5.528336097 + -4.75 Combine like terms: -5.528336097 + -4.75 = -10.278336097 x = -10.278336097 Simplifying x = -10.278336097Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.778336097, -10.278336097}
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