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Simplifying 2x = 400 + -5x2 Solving 2x = 400 + -5x2 Solving for variable 'x'. Reorder the terms: -400 + 2x + 5x2 = 400 + -5x2 + -400 + 5x2 Reorder the terms: -400 + 2x + 5x2 = 400 + -400 + -5x2 + 5x2 Combine like terms: 400 + -400 = 0 -400 + 2x + 5x2 = 0 + -5x2 + 5x2 -400 + 2x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -400 + 2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -80 + 0.4x + x2 = 0 Move the constant term to the right: Add '80' to each side of the equation. -80 + 0.4x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + 0.4x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + 0.4x + x2 = 0 + 80 0.4x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 0.4x + x2 = 80 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 80 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 80 + 0.04 Combine like terms: 80 + 0.04 = 80.04 0.04 + 0.4x + x2 = 80.04 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 80.04 Calculate the square root of the right side: 8.946507699 Break this problem into two subproblems by setting (x + 0.2) equal to 8.946507699 and -8.946507699.Subproblem 1
x + 0.2 = 8.946507699 Simplifying x + 0.2 = 8.946507699 Reorder the terms: 0.2 + x = 8.946507699 Solving 0.2 + x = 8.946507699 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 8.946507699 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 8.946507699 + -0.2 x = 8.946507699 + -0.2 Combine like terms: 8.946507699 + -0.2 = 8.746507699 x = 8.746507699 Simplifying x = 8.746507699Subproblem 2
x + 0.2 = -8.946507699 Simplifying x + 0.2 = -8.946507699 Reorder the terms: 0.2 + x = -8.946507699 Solving 0.2 + x = -8.946507699 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -8.946507699 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -8.946507699 + -0.2 x = -8.946507699 + -0.2 Combine like terms: -8.946507699 + -0.2 = -9.146507699 x = -9.146507699 Simplifying x = -9.146507699Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.746507699, -9.146507699}
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