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Simplifying 2x + 55 = (5 + 2x) * 4x Reorder the terms: 55 + 2x = (5 + 2x) * 4x Reorder the terms for easier multiplication: 55 + 2x = 4x(5 + 2x) 55 + 2x = (5 * 4x + 2x * 4x) 55 + 2x = (20x + 8x2) Solving 55 + 2x = 20x + 8x2 Solving for variable 'x'. Combine like terms: 2x + -20x = -18x 55 + -18x + -8x2 = 20x + 8x2 + -20x + -8x2 Reorder the terms: 55 + -18x + -8x2 = 20x + -20x + 8x2 + -8x2 Combine like terms: 20x + -20x = 0 55 + -18x + -8x2 = 0 + 8x2 + -8x2 55 + -18x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 55 + -18x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -6.875 + 2.25x + x2 = 0 Move the constant term to the right: Add '6.875' to each side of the equation. -6.875 + 2.25x + 6.875 + x2 = 0 + 6.875 Reorder the terms: -6.875 + 6.875 + 2.25x + x2 = 0 + 6.875 Combine like terms: -6.875 + 6.875 = 0.000 0.000 + 2.25x + x2 = 0 + 6.875 2.25x + x2 = 0 + 6.875 Combine like terms: 0 + 6.875 = 6.875 2.25x + x2 = 6.875 The x term is 2.25x. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25x + 1.265625 + x2 = 6.875 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = 6.875 + 1.265625 Combine like terms: 6.875 + 1.265625 = 8.140625 1.265625 + 2.25x + x2 = 8.140625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 8.140625 Calculate the square root of the right side: 2.853178053 Break this problem into two subproblems by setting (x + 1.125) equal to 2.853178053 and -2.853178053.Subproblem 1
x + 1.125 = 2.853178053 Simplifying x + 1.125 = 2.853178053 Reorder the terms: 1.125 + x = 2.853178053 Solving 1.125 + x = 2.853178053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = 2.853178053 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 2.853178053 + -1.125 x = 2.853178053 + -1.125 Combine like terms: 2.853178053 + -1.125 = 1.728178053 x = 1.728178053 Simplifying x = 1.728178053Subproblem 2
x + 1.125 = -2.853178053 Simplifying x + 1.125 = -2.853178053 Reorder the terms: 1.125 + x = -2.853178053 Solving 1.125 + x = -2.853178053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = -2.853178053 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -2.853178053 + -1.125 x = -2.853178053 + -1.125 Combine like terms: -2.853178053 + -1.125 = -3.978178053 x = -3.978178053 Simplifying x = -3.978178053Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.728178053, -3.978178053}
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