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Simplifying 5x(2x + -89) = 164 Reorder the terms: 5x(-89 + 2x) = 164 (-89 * 5x + 2x * 5x) = 164 (-445x + 10x2) = 164 Solving -445x + 10x2 = 164 Solving for variable 'x'. Reorder the terms: -164 + -445x + 10x2 = 164 + -164 Combine like terms: 164 + -164 = 0 -164 + -445x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -16.4 + -44.5x + x2 = 0.0 Move the constant term to the right: Add '16.4' to each side of the equation. -16.4 + -44.5x + 16.4 + x2 = 0.0 + 16.4 Reorder the terms: -16.4 + 16.4 + -44.5x + x2 = 0.0 + 16.4 Combine like terms: -16.4 + 16.4 = 0.0 0.0 + -44.5x + x2 = 0.0 + 16.4 -44.5x + x2 = 0.0 + 16.4 Combine like terms: 0.0 + 16.4 = 16.4 -44.5x + x2 = 16.4 The x term is -44.5x. Take half its coefficient (-22.25). Square it (495.0625) and add it to both sides. Add '495.0625' to each side of the equation. -44.5x + 495.0625 + x2 = 16.4 + 495.0625 Reorder the terms: 495.0625 + -44.5x + x2 = 16.4 + 495.0625 Combine like terms: 16.4 + 495.0625 = 511.4625 495.0625 + -44.5x + x2 = 511.4625 Factor a perfect square on the left side: (x + -22.25)(x + -22.25) = 511.4625 Calculate the square root of the right side: 22.615536695 Break this problem into two subproblems by setting (x + -22.25) equal to 22.615536695 and -22.615536695.Subproblem 1
x + -22.25 = 22.615536695 Simplifying x + -22.25 = 22.615536695 Reorder the terms: -22.25 + x = 22.615536695 Solving -22.25 + x = 22.615536695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.25' to each side of the equation. -22.25 + 22.25 + x = 22.615536695 + 22.25 Combine like terms: -22.25 + 22.25 = 0.00 0.00 + x = 22.615536695 + 22.25 x = 22.615536695 + 22.25 Combine like terms: 22.615536695 + 22.25 = 44.865536695 x = 44.865536695 Simplifying x = 44.865536695Subproblem 2
x + -22.25 = -22.615536695 Simplifying x + -22.25 = -22.615536695 Reorder the terms: -22.25 + x = -22.615536695 Solving -22.25 + x = -22.615536695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.25' to each side of the equation. -22.25 + 22.25 + x = -22.615536695 + 22.25 Combine like terms: -22.25 + 22.25 = 0.00 0.00 + x = -22.615536695 + 22.25 x = -22.615536695 + 22.25 Combine like terms: -22.615536695 + 22.25 = -0.365536695 x = -0.365536695 Simplifying x = -0.365536695Solution
The solution to the problem is based on the solutions from the subproblems. x = {44.865536695, -0.365536695}
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