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Simplifying 5x2 + 11x + -500 = 0 Reorder the terms: -500 + 11x + 5x2 = 0 Solving -500 + 11x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -100 + 2.2x + x2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + 2.2x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 2.2x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 2.2x + x2 = 0 + 100 2.2x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 2.2x + x2 = 100 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 = 100 + 1.21 Reorder the terms: 1.21 + 2.2x + x2 = 100 + 1.21 Combine like terms: 100 + 1.21 = 101.21 1.21 + 2.2x + x2 = 101.21 Factor a perfect square on the left side: (x + 1.1)(x + 1.1) = 101.21 Calculate the square root of the right side: 10.060318086 Break this problem into two subproblems by setting (x + 1.1) equal to 10.060318086 and -10.060318086.Subproblem 1
x + 1.1 = 10.060318086 Simplifying x + 1.1 = 10.060318086 Reorder the terms: 1.1 + x = 10.060318086 Solving 1.1 + x = 10.060318086 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 = 10.060318086 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = 10.060318086 + -1.1 x = 10.060318086 + -1.1 Combine like terms: 10.060318086 + -1.1 = 8.960318086 x = 8.960318086 Simplifying x = 8.960318086Subproblem 2
x + 1.1 = -10.060318086 Simplifying x + 1.1 = -10.060318086 Reorder the terms: 1.1 + x = -10.060318086 Solving 1.1 + x = -10.060318086 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 = -10.060318086 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = -10.060318086 + -1.1 x = -10.060318086 + -1.1 Combine like terms: -10.060318086 + -1.1 = -11.160318086 x = -11.160318086 Simplifying x = -11.160318086Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.960318086, -11.160318086}
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