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Simplifying (5x2) + 4x + -25 = 0 Reorder the terms: -25 + 4x + (5x2) = 0 Solving -25 + 4x + (5x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5 + 0.8x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 0.8x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 0.8x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 0.8x + x2 = 0 + 5 0.8x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 0.8x + x2 = 5 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = 5 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 5 + 0.16 Combine like terms: 5 + 0.16 = 5.16 0.16 + 0.8x + x2 = 5.16 Factor a perfect square on the left side: ((x) + 0.4)((x) + 0.4) = 5.16 Calculate the square root of the right side: 2.271563338 Break this problem into two subproblems by setting ((x) + 0.4) equal to 2.271563338 and -2.271563338.Subproblem 1
(x) + 0.4 = 2.271563338 Simplifying (x) + 0.4 = 2.271563338 x + 0.4 = 2.271563338 Reorder the terms: 0.4 + x = 2.271563338 Solving 0.4 + x = 2.271563338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 2.271563338 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 2.271563338 + -0.4 x = 2.271563338 + -0.4 Combine like terms: 2.271563338 + -0.4 = 1.871563338 x = 1.871563338 Simplifying x = 1.871563338Subproblem 2
(x) + 0.4 = -2.271563338 Simplifying (x) + 0.4 = -2.271563338 x + 0.4 = -2.271563338 Reorder the terms: 0.4 + x = -2.271563338 Solving 0.4 + x = -2.271563338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -2.271563338 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -2.271563338 + -0.4 x = -2.271563338 + -0.4 Combine like terms: -2.271563338 + -0.4 = -2.671563338 x = -2.671563338 Simplifying x = -2.671563338Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.871563338, -2.671563338}
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