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Simplifying x(19 + 2x) = 28 (19 * x + 2x * x) = 28 (19x + 2x2) = 28 Solving 19x + 2x2 = 28 Solving for variable 'x'. Reorder the terms: -28 + 19x + 2x2 = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + 19x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -14 + 9.5x + x2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + 9.5x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + 9.5x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 9.5x + x2 = 0 + 14 9.5x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 9.5x + x2 = 14 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 = 14 + 22.5625 Reorder the terms: 22.5625 + 9.5x + x2 = 14 + 22.5625 Combine like terms: 14 + 22.5625 = 36.5625 22.5625 + 9.5x + x2 = 36.5625 Factor a perfect square on the left side: (x + 4.75)(x + 4.75) = 36.5625 Calculate the square root of the right side: 6.046693311 Break this problem into two subproblems by setting (x + 4.75) equal to 6.046693311 and -6.046693311.Subproblem 1
x + 4.75 = 6.046693311 Simplifying x + 4.75 = 6.046693311 Reorder the terms: 4.75 + x = 6.046693311 Solving 4.75 + x = 6.046693311 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 = 6.046693311 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = 6.046693311 + -4.75 x = 6.046693311 + -4.75 Combine like terms: 6.046693311 + -4.75 = 1.296693311 x = 1.296693311 Simplifying x = 1.296693311Subproblem 2
x + 4.75 = -6.046693311 Simplifying x + 4.75 = -6.046693311 Reorder the terms: 4.75 + x = -6.046693311 Solving 4.75 + x = -6.046693311 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 = -6.046693311 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = -6.046693311 + -4.75 x = -6.046693311 + -4.75 Combine like terms: -6.046693311 + -4.75 = -10.796693311 x = -10.796693311 Simplifying x = -10.796693311Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.296693311, -10.796693311}
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