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Simplifying 25x2 + 4x + -1.5164 = 0 Reorder the terms: -1.5164 + 4x + 25x2 = 0 Solving -1.5164 + 4x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.060656 + 0.16x + x2 = 0 Move the constant term to the right: Add '0.060656' to each side of the equation. -0.060656 + 0.16x + 0.060656 + x2 = 0 + 0.060656 Reorder the terms: -0.060656 + 0.060656 + 0.16x + x2 = 0 + 0.060656 Combine like terms: -0.060656 + 0.060656 = 0.000000 0.000000 + 0.16x + x2 = 0 + 0.060656 0.16x + x2 = 0 + 0.060656 Combine like terms: 0 + 0.060656 = 0.060656 0.16x + x2 = 0.060656 The x term is 0.16x. Take half its coefficient (0.08). Square it (0.0064) and add it to both sides. Add '0.0064' to each side of the equation. 0.16x + 0.0064 + x2 = 0.060656 + 0.0064 Reorder the terms: 0.0064 + 0.16x + x2 = 0.060656 + 0.0064 Combine like terms: 0.060656 + 0.0064 = 0.067056 0.0064 + 0.16x + x2 = 0.067056 Factor a perfect square on the left side: (x + 0.08)(x + 0.08) = 0.067056 Calculate the square root of the right side: 0.258951733 Break this problem into two subproblems by setting (x + 0.08) equal to 0.258951733 and -0.258951733.Subproblem 1
x + 0.08 = 0.258951733 Simplifying x + 0.08 = 0.258951733 Reorder the terms: 0.08 + x = 0.258951733 Solving 0.08 + x = 0.258951733 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08' to each side of the equation. 0.08 + -0.08 + x = 0.258951733 + -0.08 Combine like terms: 0.08 + -0.08 = 0.00 0.00 + x = 0.258951733 + -0.08 x = 0.258951733 + -0.08 Combine like terms: 0.258951733 + -0.08 = 0.178951733 x = 0.178951733 Simplifying x = 0.178951733Subproblem 2
x + 0.08 = -0.258951733 Simplifying x + 0.08 = -0.258951733 Reorder the terms: 0.08 + x = -0.258951733 Solving 0.08 + x = -0.258951733 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08' to each side of the equation. 0.08 + -0.08 + x = -0.258951733 + -0.08 Combine like terms: 0.08 + -0.08 = 0.00 0.00 + x = -0.258951733 + -0.08 x = -0.258951733 + -0.08 Combine like terms: -0.258951733 + -0.08 = -0.338951733 x = -0.338951733 Simplifying x = -0.338951733Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.178951733, -0.338951733}
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