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Simplifying 19x + 17 = 4x2 + 8x + 16 Reorder the terms: 17 + 19x = 4x2 + 8x + 16 Reorder the terms: 17 + 19x = 16 + 8x + 4x2 Solving 17 + 19x = 16 + 8x + 4x2 Solving for variable 'x'. Reorder the terms: 17 + -16 + 19x + -8x + -4x2 = 16 + 8x + 4x2 + -16 + -8x + -4x2 Combine like terms: 17 + -16 = 1 1 + 19x + -8x + -4x2 = 16 + 8x + 4x2 + -16 + -8x + -4x2 Combine like terms: 19x + -8x = 11x 1 + 11x + -4x2 = 16 + 8x + 4x2 + -16 + -8x + -4x2 Reorder the terms: 1 + 11x + -4x2 = 16 + -16 + 8x + -8x + 4x2 + -4x2 Combine like terms: 16 + -16 = 0 1 + 11x + -4x2 = 0 + 8x + -8x + 4x2 + -4x2 1 + 11x + -4x2 = 8x + -8x + 4x2 + -4x2 Combine like terms: 8x + -8x = 0 1 + 11x + -4x2 = 0 + 4x2 + -4x2 1 + 11x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 1 + 11x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.25 + -2.75x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -2.75x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -2.75x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -2.75x + x2 = 0 + 0.25 -2.75x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -2.75x + x2 = 0.25 The x term is -2.75x. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75x + 1.890625 + x2 = 0.25 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = 0.25 + 1.890625 Combine like terms: 0.25 + 1.890625 = 2.140625 1.890625 + -2.75x + x2 = 2.140625 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = 2.140625 Calculate the square root of the right side: 1.463087489 Break this problem into two subproblems by setting (x + -1.375) equal to 1.463087489 and -1.463087489.Subproblem 1
x + -1.375 = 1.463087489 Simplifying x + -1.375 = 1.463087489 Reorder the terms: -1.375 + x = 1.463087489 Solving -1.375 + x = 1.463087489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = 1.463087489 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 1.463087489 + 1.375 x = 1.463087489 + 1.375 Combine like terms: 1.463087489 + 1.375 = 2.838087489 x = 2.838087489 Simplifying x = 2.838087489Subproblem 2
x + -1.375 = -1.463087489 Simplifying x + -1.375 = -1.463087489 Reorder the terms: -1.375 + x = -1.463087489 Solving -1.375 + x = -1.463087489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = -1.463087489 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -1.463087489 + 1.375 x = -1.463087489 + 1.375 Combine like terms: -1.463087489 + 1.375 = -0.088087489 x = -0.088087489 Simplifying x = -0.088087489Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.838087489, -0.088087489}
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