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Simplifying 2x2 + 19x + -4.5 = 0 Reorder the terms: -4.5 + 19x + 2x2 = 0 Solving -4.5 + 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'. -2.25 + 9.5x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + 9.5x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + 9.5x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + 9.5x + x2 = 0 + 2.25 9.5x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 9.5x + x2 = 2.25 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 = 2.25 + 22.5625 Reorder the terms: 22.5625 + 9.5x + x2 = 2.25 + 22.5625 Combine like terms: 2.25 + 22.5625 = 24.8125 22.5625 + 9.5x + x2 = 24.8125 Factor a perfect square on the left side: (x + 4.75)(x + 4.75) = 24.8125 Calculate the square root of the right side: 4.981214711 Break this problem into two subproblems by setting (x + 4.75) equal to 4.981214711 and -4.981214711.Subproblem 1
x + 4.75 = 4.981214711 Simplifying x + 4.75 = 4.981214711 Reorder the terms: 4.75 + x = 4.981214711 Solving 4.75 + x = 4.981214711 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 = 4.981214711 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = 4.981214711 + -4.75 x = 4.981214711 + -4.75 Combine like terms: 4.981214711 + -4.75 = 0.231214711 x = 0.231214711 Simplifying x = 0.231214711Subproblem 2
x + 4.75 = -4.981214711 Simplifying x + 4.75 = -4.981214711 Reorder the terms: 4.75 + x = -4.981214711 Solving 4.75 + x = -4.981214711 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 = -4.981214711 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = -4.981214711 + -4.75 x = -4.981214711 + -4.75 Combine like terms: -4.981214711 + -4.75 = -9.731214711 x = -9.731214711 Simplifying x = -9.731214711Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.231214711, -9.731214711}
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