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Simplifying 5x2 + 2x = 569 Reorder the terms: 2x + 5x2 = 569 Solving 2x + 5x2 = 569 Solving for variable 'x'. Reorder the terms: -569 + 2x + 5x2 = 569 + -569 Combine like terms: 569 + -569 = 0 -569 + 2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -113.8 + 0.4x + x2 = 0 Move the constant term to the right: Add '113.8' to each side of the equation. -113.8 + 0.4x + 113.8 + x2 = 0 + 113.8 Reorder the terms: -113.8 + 113.8 + 0.4x + x2 = 0 + 113.8 Combine like terms: -113.8 + 113.8 = 0.0 0.0 + 0.4x + x2 = 0 + 113.8 0.4x + x2 = 0 + 113.8 Combine like terms: 0 + 113.8 = 113.8 0.4x + x2 = 113.8 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 = 113.8 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 113.8 + 0.04 Combine like terms: 113.8 + 0.04 = 113.84 0.04 + 0.4x + x2 = 113.84 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 113.84 Calculate the square root of the right side: 10.669582935 Break this problem into two subproblems by setting (x + 0.2) equal to 10.669582935 and -10.669582935.Subproblem 1
x + 0.2 = 10.669582935 Simplifying x + 0.2 = 10.669582935 Reorder the terms: 0.2 + x = 10.669582935 Solving 0.2 + x = 10.669582935 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 = 10.669582935 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 10.669582935 + -0.2 x = 10.669582935 + -0.2 Combine like terms: 10.669582935 + -0.2 = 10.469582935 x = 10.469582935 Simplifying x = 10.469582935Subproblem 2
x + 0.2 = -10.669582935 Simplifying x + 0.2 = -10.669582935 Reorder the terms: 0.2 + x = -10.669582935 Solving 0.2 + x = -10.669582935 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 = -10.669582935 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -10.669582935 + -0.2 x = -10.669582935 + -0.2 Combine like terms: -10.669582935 + -0.2 = -10.869582935 x = -10.869582935 Simplifying x = -10.869582935Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.469582935, -10.869582935}
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