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Simplifying 2x2 + 19x = 32 Reorder the terms: 19x + 2x2 = 32 Solving 19x + 2x2 = 32 Solving for variable 'x'. Reorder the terms: -32 + 19x + 2x2 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + 19x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -16 + 9.5x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + 9.5x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 9.5x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 9.5x + x2 = 0 + 16 9.5x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 9.5x + x2 = 16 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 = 16 + 22.5625 Reorder the terms: 22.5625 + 9.5x + x2 = 16 + 22.5625 Combine like terms: 16 + 22.5625 = 38.5625 22.5625 + 9.5x + x2 = 38.5625 Factor a perfect square on the left side: (x + 4.75)(x + 4.75) = 38.5625 Calculate the square root of the right side: 6.209871174 Break this problem into two subproblems by setting (x + 4.75) equal to 6.209871174 and -6.209871174.Subproblem 1
x + 4.75 = 6.209871174 Simplifying x + 4.75 = 6.209871174 Reorder the terms: 4.75 + x = 6.209871174 Solving 4.75 + x = 6.209871174 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 = 6.209871174 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = 6.209871174 + -4.75 x = 6.209871174 + -4.75 Combine like terms: 6.209871174 + -4.75 = 1.459871174 x = 1.459871174 Simplifying x = 1.459871174Subproblem 2
x + 4.75 = -6.209871174 Simplifying x + 4.75 = -6.209871174 Reorder the terms: 4.75 + x = -6.209871174 Solving 4.75 + x = -6.209871174 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 = -6.209871174 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = -6.209871174 + -4.75 x = -6.209871174 + -4.75 Combine like terms: -6.209871174 + -4.75 = -10.959871174 x = -10.959871174 Simplifying x = -10.959871174Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.459871174, -10.959871174}
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