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Simplifying 25x2 + 56x + 4 = 5 Reorder the terms: 4 + 56x + 25x2 = 5 Solving 4 + 56x + 25x2 = 5 Solving for variable 'x'. Reorder the terms: 4 + -5 + 56x + 25x2 = 5 + -5 Combine like terms: 4 + -5 = -1 -1 + 56x + 25x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -1 + 56x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.04 + 2.24x + x2 = 0 Move the constant term to the right: Add '0.04' to each side of the equation. -0.04 + 2.24x + 0.04 + x2 = 0 + 0.04 Reorder the terms: -0.04 + 0.04 + 2.24x + x2 = 0 + 0.04 Combine like terms: -0.04 + 0.04 = 0.00 0.00 + 2.24x + x2 = 0 + 0.04 2.24x + x2 = 0 + 0.04 Combine like terms: 0 + 0.04 = 0.04 2.24x + x2 = 0.04 The x term is 2.24x. Take half its coefficient (1.12). Square it (1.2544) and add it to both sides. Add '1.2544' to each side of the equation. 2.24x + 1.2544 + x2 = 0.04 + 1.2544 Reorder the terms: 1.2544 + 2.24x + x2 = 0.04 + 1.2544 Combine like terms: 0.04 + 1.2544 = 1.2944 1.2544 + 2.24x + x2 = 1.2944 Factor a perfect square on the left side: (x + 1.12)(x + 1.12) = 1.2944 Calculate the square root of the right side: 1.137717012 Break this problem into two subproblems by setting (x + 1.12) equal to 1.137717012 and -1.137717012.Subproblem 1
x + 1.12 = 1.137717012 Simplifying x + 1.12 = 1.137717012 Reorder the terms: 1.12 + x = 1.137717012 Solving 1.12 + x = 1.137717012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.12' to each side of the equation. 1.12 + -1.12 + x = 1.137717012 + -1.12 Combine like terms: 1.12 + -1.12 = 0.00 0.00 + x = 1.137717012 + -1.12 x = 1.137717012 + -1.12 Combine like terms: 1.137717012 + -1.12 = 0.017717012 x = 0.017717012 Simplifying x = 0.017717012Subproblem 2
x + 1.12 = -1.137717012 Simplifying x + 1.12 = -1.137717012 Reorder the terms: 1.12 + x = -1.137717012 Solving 1.12 + x = -1.137717012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.12' to each side of the equation. 1.12 + -1.12 + x = -1.137717012 + -1.12 Combine like terms: 1.12 + -1.12 = 0.00 0.00 + x = -1.137717012 + -1.12 x = -1.137717012 + -1.12 Combine like terms: -1.137717012 + -1.12 = -2.257717012 x = -2.257717012 Simplifying x = -2.257717012Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.017717012, -2.257717012}
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