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Simplifying 5x2 + -82x = 200 Reorder the terms: -82x + 5x2 = 200 Solving -82x + 5x2 = 200 Solving for variable 'x'. Reorder the terms: -200 + -82x + 5x2 = 200 + -200 Combine like terms: 200 + -200 = 0 -200 + -82x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -40 + -16.4x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + -16.4x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + -16.4x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -16.4x + x2 = 0 + 40 -16.4x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 -16.4x + x2 = 40 The x term is -16.4x. Take half its coefficient (-8.2). Square it (67.24) and add it to both sides. Add '67.24' to each side of the equation. -16.4x + 67.24 + x2 = 40 + 67.24 Reorder the terms: 67.24 + -16.4x + x2 = 40 + 67.24 Combine like terms: 40 + 67.24 = 107.24 67.24 + -16.4x + x2 = 107.24 Factor a perfect square on the left side: (x + -8.2)(x + -8.2) = 107.24 Calculate the square root of the right side: 10.355674773 Break this problem into two subproblems by setting (x + -8.2) equal to 10.355674773 and -10.355674773.Subproblem 1
x + -8.2 = 10.355674773 Simplifying x + -8.2 = 10.355674773 Reorder the terms: -8.2 + x = 10.355674773 Solving -8.2 + x = 10.355674773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.2' to each side of the equation. -8.2 + 8.2 + x = 10.355674773 + 8.2 Combine like terms: -8.2 + 8.2 = 0.0 0.0 + x = 10.355674773 + 8.2 x = 10.355674773 + 8.2 Combine like terms: 10.355674773 + 8.2 = 18.555674773 x = 18.555674773 Simplifying x = 18.555674773Subproblem 2
x + -8.2 = -10.355674773 Simplifying x + -8.2 = -10.355674773 Reorder the terms: -8.2 + x = -10.355674773 Solving -8.2 + x = -10.355674773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.2' to each side of the equation. -8.2 + 8.2 + x = -10.355674773 + 8.2 Combine like terms: -8.2 + 8.2 = 0.0 0.0 + x = -10.355674773 + 8.2 x = -10.355674773 + 8.2 Combine like terms: -10.355674773 + 8.2 = -2.155674773 x = -2.155674773 Simplifying x = -2.155674773Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.555674773, -2.155674773}
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