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Simplifying 0.04x2 + 8x + 200 = 0 Reorder the terms: 200 + 8x + 0.04x2 = 0 Solving 200 + 8x + 0.04x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.04 the coefficient of the squared term: Divide each side by '0.04'. 5000 + 200x + x2 = 0 Move the constant term to the right: Add '-5000' to each side of the equation. 5000 + 200x + -5000 + x2 = 0 + -5000 Reorder the terms: 5000 + -5000 + 200x + x2 = 0 + -5000 Combine like terms: 5000 + -5000 = 0 0 + 200x + x2 = 0 + -5000 200x + x2 = 0 + -5000 Combine like terms: 0 + -5000 = -5000 200x + x2 = -5000 The x term is 200x. Take half its coefficient (100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. 200x + 10000 + x2 = -5000 + 10000 Reorder the terms: 10000 + 200x + x2 = -5000 + 10000 Combine like terms: -5000 + 10000 = 5000 10000 + 200x + x2 = 5000 Factor a perfect square on the left side: (x + 100)(x + 100) = 5000 Calculate the square root of the right side: 70.710678119 Break this problem into two subproblems by setting (x + 100) equal to 70.710678119 and -70.710678119.Subproblem 1
x + 100 = 70.710678119 Simplifying x + 100 = 70.710678119 Reorder the terms: 100 + x = 70.710678119 Solving 100 + x = 70.710678119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + x = 70.710678119 + -100 Combine like terms: 100 + -100 = 0 0 + x = 70.710678119 + -100 x = 70.710678119 + -100 Combine like terms: 70.710678119 + -100 = -29.289321881 x = -29.289321881 Simplifying x = -29.289321881Subproblem 2
x + 100 = -70.710678119 Simplifying x + 100 = -70.710678119 Reorder the terms: 100 + x = -70.710678119 Solving 100 + x = -70.710678119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + x = -70.710678119 + -100 Combine like terms: 100 + -100 = 0 0 + x = -70.710678119 + -100 x = -70.710678119 + -100 Combine like terms: -70.710678119 + -100 = -170.710678119 x = -170.710678119 Simplifying x = -170.710678119Solution
The solution to the problem is based on the solutions from the subproblems. x = {-29.289321881, -170.710678119}
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