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Simplifying 20x2 + 18x + -27 = 0 Reorder the terms: -27 + 18x + 20x2 = 0 Solving -27 + 18x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -1.35 + 0.9x + x2 = 0 Move the constant term to the right: Add '1.35' to each side of the equation. -1.35 + 0.9x + 1.35 + x2 = 0 + 1.35 Reorder the terms: -1.35 + 1.35 + 0.9x + x2 = 0 + 1.35 Combine like terms: -1.35 + 1.35 = 0.00 0.00 + 0.9x + x2 = 0 + 1.35 0.9x + x2 = 0 + 1.35 Combine like terms: 0 + 1.35 = 1.35 0.9x + x2 = 1.35 The x term is 0.9x. Take half its coefficient (0.45). Square it (0.2025) and add it to both sides. Add '0.2025' to each side of the equation. 0.9x + 0.2025 + x2 = 1.35 + 0.2025 Reorder the terms: 0.2025 + 0.9x + x2 = 1.35 + 0.2025 Combine like terms: 1.35 + 0.2025 = 1.5525 0.2025 + 0.9x + x2 = 1.5525 Factor a perfect square on the left side: (x + 0.45)(x + 0.45) = 1.5525 Calculate the square root of the right side: 1.245993579 Break this problem into two subproblems by setting (x + 0.45) equal to 1.245993579 and -1.245993579.Subproblem 1
x + 0.45 = 1.245993579 Simplifying x + 0.45 = 1.245993579 Reorder the terms: 0.45 + x = 1.245993579 Solving 0.45 + x = 1.245993579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + x = 1.245993579 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + x = 1.245993579 + -0.45 x = 1.245993579 + -0.45 Combine like terms: 1.245993579 + -0.45 = 0.795993579 x = 0.795993579 Simplifying x = 0.795993579Subproblem 2
x + 0.45 = -1.245993579 Simplifying x + 0.45 = -1.245993579 Reorder the terms: 0.45 + x = -1.245993579 Solving 0.45 + x = -1.245993579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + x = -1.245993579 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + x = -1.245993579 + -0.45 x = -1.245993579 + -0.45 Combine like terms: -1.245993579 + -0.45 = -1.695993579 x = -1.695993579 Simplifying x = -1.695993579Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.795993579, -1.695993579}
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