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Simplifying 25 + 56x = 25x2 + -3 + x Reorder the terms: 25 + 56x = -3 + x + 25x2 Solving 25 + 56x = -3 + x + 25x2 Solving for variable 'x'. Reorder the terms: 25 + 3 + 56x + -1x + -25x2 = -3 + x + 25x2 + 3 + -1x + -25x2 Combine like terms: 25 + 3 = 28 28 + 56x + -1x + -25x2 = -3 + x + 25x2 + 3 + -1x + -25x2 Combine like terms: 56x + -1x = 55x 28 + 55x + -25x2 = -3 + x + 25x2 + 3 + -1x + -25x2 Reorder the terms: 28 + 55x + -25x2 = -3 + 3 + x + -1x + 25x2 + -25x2 Combine like terms: -3 + 3 = 0 28 + 55x + -25x2 = 0 + x + -1x + 25x2 + -25x2 28 + 55x + -25x2 = x + -1x + 25x2 + -25x2 Combine like terms: x + -1x = 0 28 + 55x + -25x2 = 0 + 25x2 + -25x2 28 + 55x + -25x2 = 25x2 + -25x2 Combine like terms: 25x2 + -25x2 = 0 28 + 55x + -25x2 = 0 Begin completing the square. Divide all terms by -25 the coefficient of the squared term: Divide each side by '-25'. -1.12 + -2.2x + x2 = 0 Move the constant term to the right: Add '1.12' to each side of the equation. -1.12 + -2.2x + 1.12 + x2 = 0 + 1.12 Reorder the terms: -1.12 + 1.12 + -2.2x + x2 = 0 + 1.12 Combine like terms: -1.12 + 1.12 = 0.00 0.00 + -2.2x + x2 = 0 + 1.12 -2.2x + x2 = 0 + 1.12 Combine like terms: 0 + 1.12 = 1.12 -2.2x + x2 = 1.12 The x term is -2.2x. Take half its coefficient (-1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. -2.2x + 1.21 + x2 = 1.12 + 1.21 Reorder the terms: 1.21 + -2.2x + x2 = 1.12 + 1.21 Combine like terms: 1.12 + 1.21 = 2.33 1.21 + -2.2x + x2 = 2.33 Factor a perfect square on the left side: (x + -1.1)(x + -1.1) = 2.33 Calculate the square root of the right side: 1.526433752 Break this problem into two subproblems by setting (x + -1.1) equal to 1.526433752 and -1.526433752.Subproblem 1
x + -1.1 = 1.526433752 Simplifying x + -1.1 = 1.526433752 Reorder the terms: -1.1 + x = 1.526433752 Solving -1.1 + x = 1.526433752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = 1.526433752 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = 1.526433752 + 1.1 x = 1.526433752 + 1.1 Combine like terms: 1.526433752 + 1.1 = 2.626433752 x = 2.626433752 Simplifying x = 2.626433752Subproblem 2
x + -1.1 = -1.526433752 Simplifying x + -1.1 = -1.526433752 Reorder the terms: -1.1 + x = -1.526433752 Solving -1.1 + x = -1.526433752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = -1.526433752 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = -1.526433752 + 1.1 x = -1.526433752 + 1.1 Combine like terms: -1.526433752 + 1.1 = -0.426433752 x = -0.426433752 Simplifying x = -0.426433752Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.626433752, -0.426433752}
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