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Simplifying 5x2 + 4x + 1 = 25 Reorder the terms: 1 + 4x + 5x2 = 25 Solving 1 + 4x + 5x2 = 25 Solving for variable 'x'. Reorder the terms: 1 + -25 + 4x + 5x2 = 25 + -25 Combine like terms: 1 + -25 = -24 -24 + 4x + 5x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -24 + 4x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.8 + 0.8x + x2 = 0 Move the constant term to the right: Add '4.8' to each side of the equation. -4.8 + 0.8x + 4.8 + x2 = 0 + 4.8 Reorder the terms: -4.8 + 4.8 + 0.8x + x2 = 0 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + 0.8x + x2 = 0 + 4.8 0.8x + x2 = 0 + 4.8 Combine like terms: 0 + 4.8 = 4.8 0.8x + x2 = 4.8 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 = 4.8 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 4.8 + 0.16 Combine like terms: 4.8 + 0.16 = 4.96 0.16 + 0.8x + x2 = 4.96 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 4.96 Calculate the square root of the right side: 2.227105745 Break this problem into two subproblems by setting (x + 0.4) equal to 2.227105745 and -2.227105745.Subproblem 1
x + 0.4 = 2.227105745 Simplifying x + 0.4 = 2.227105745 Reorder the terms: 0.4 + x = 2.227105745 Solving 0.4 + x = 2.227105745 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 = 2.227105745 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 2.227105745 + -0.4 x = 2.227105745 + -0.4 Combine like terms: 2.227105745 + -0.4 = 1.827105745 x = 1.827105745 Simplifying x = 1.827105745Subproblem 2
x + 0.4 = -2.227105745 Simplifying x + 0.4 = -2.227105745 Reorder the terms: 0.4 + x = -2.227105745 Solving 0.4 + x = -2.227105745 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 = -2.227105745 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -2.227105745 + -0.4 x = -2.227105745 + -0.4 Combine like terms: -2.227105745 + -0.4 = -2.627105745 x = -2.627105745 Simplifying x = -2.627105745Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.827105745, -2.627105745}
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