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Simplifying 0 = -2x2 + 40x + 5 Reorder the terms: 0 = 5 + 40x + -2x2 Solving 0 = 5 + 40x + -2x2 Solving for variable 'x'. Combine like terms: 0 + -5 = -5 -5 + -40x + 2x2 = 5 + 40x + -2x2 + -5 + -40x + 2x2 Reorder the terms: -5 + -40x + 2x2 = 5 + -5 + 40x + -40x + -2x2 + 2x2 Combine like terms: 5 + -5 = 0 -5 + -40x + 2x2 = 0 + 40x + -40x + -2x2 + 2x2 -5 + -40x + 2x2 = 40x + -40x + -2x2 + 2x2 Combine like terms: 40x + -40x = 0 -5 + -40x + 2x2 = 0 + -2x2 + 2x2 -5 + -40x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -5 + -40x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + -20x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -20x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -20x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -20x + x2 = 0 + 2.5 -20x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -20x + x2 = 2.5 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = 2.5 + 100 Reorder the terms: 100 + -20x + x2 = 2.5 + 100 Combine like terms: 2.5 + 100 = 102.5 100 + -20x + x2 = 102.5 Factor a perfect square on the left side: (x + -10)(x + -10) = 102.5 Calculate the square root of the right side: 10.124228366 Break this problem into two subproblems by setting (x + -10) equal to 10.124228366 and -10.124228366.Subproblem 1
x + -10 = 10.124228366 Simplifying x + -10 = 10.124228366 Reorder the terms: -10 + x = 10.124228366 Solving -10 + x = 10.124228366 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 10.124228366 + 10 Combine like terms: -10 + 10 = 0 0 + x = 10.124228366 + 10 x = 10.124228366 + 10 Combine like terms: 10.124228366 + 10 = 20.124228366 x = 20.124228366 Simplifying x = 20.124228366Subproblem 2
x + -10 = -10.124228366 Simplifying x + -10 = -10.124228366 Reorder the terms: -10 + x = -10.124228366 Solving -10 + x = -10.124228366 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -10.124228366 + 10 Combine like terms: -10 + 10 = 0 0 + x = -10.124228366 + 10 x = -10.124228366 + 10 Combine like terms: -10.124228366 + 10 = -0.124228366 x = -0.124228366 Simplifying x = -0.124228366Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.124228366, -0.124228366}
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