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Simplifying 5x2 + 11x = 20 Reorder the terms: 11x + 5x2 = 20 Solving 11x + 5x2 = 20 Solving for variable 'x'. Reorder the terms: -20 + 11x + 5x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + 11x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4 + 2.2x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 2.2x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 2.2x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 2.2x + x2 = 0 + 4 2.2x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 2.2x + x2 = 4 The x term is 2.2x. Take half its coefficient (1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. 2.2x + 1.21 + x2 = 4 + 1.21 Reorder the terms: 1.21 + 2.2x + x2 = 4 + 1.21 Combine like terms: 4 + 1.21 = 5.21 1.21 + 2.2x + x2 = 5.21 Factor a perfect square on the left side: (x + 1.1)(x + 1.1) = 5.21 Calculate the square root of the right side: 2.282542442 Break this problem into two subproblems by setting (x + 1.1) equal to 2.282542442 and -2.282542442.Subproblem 1
x + 1.1 = 2.282542442 Simplifying x + 1.1 = 2.282542442 Reorder the terms: 1.1 + x = 2.282542442 Solving 1.1 + x = 2.282542442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + x = 2.282542442 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = 2.282542442 + -1.1 x = 2.282542442 + -1.1 Combine like terms: 2.282542442 + -1.1 = 1.182542442 x = 1.182542442 Simplifying x = 1.182542442Subproblem 2
x + 1.1 = -2.282542442 Simplifying x + 1.1 = -2.282542442 Reorder the terms: 1.1 + x = -2.282542442 Solving 1.1 + x = -2.282542442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + x = -2.282542442 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = -2.282542442 + -1.1 x = -2.282542442 + -1.1 Combine like terms: -2.282542442 + -1.1 = -3.382542442 x = -3.382542442 Simplifying x = -3.382542442Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.182542442, -3.382542442}
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