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Simplifying 1x + 3 = 25x2 + -4x Reorder the terms: 3 + 1x = 25x2 + -4x Reorder the terms: 3 + 1x = -4x + 25x2 Solving 3 + 1x = -4x + 25x2 Solving for variable 'x'. Combine like terms: 1x + 4x = 5x 3 + 5x + -25x2 = -4x + 25x2 + 4x + -25x2 Reorder the terms: 3 + 5x + -25x2 = -4x + 4x + 25x2 + -25x2 Combine like terms: -4x + 4x = 0 3 + 5x + -25x2 = 0 + 25x2 + -25x2 3 + 5x + -25x2 = 25x2 + -25x2 Combine like terms: 25x2 + -25x2 = 0 3 + 5x + -25x2 = 0 Begin completing the square. Divide all terms by -25 the coefficient of the squared term: Divide each side by '-25'. -0.12 + -0.2x + x2 = 0 Move the constant term to the right: Add '0.12' to each side of the equation. -0.12 + -0.2x + 0.12 + x2 = 0 + 0.12 Reorder the terms: -0.12 + 0.12 + -0.2x + x2 = 0 + 0.12 Combine like terms: -0.12 + 0.12 = 0.00 0.00 + -0.2x + x2 = 0 + 0.12 -0.2x + x2 = 0 + 0.12 Combine like terms: 0 + 0.12 = 0.12 -0.2x + x2 = 0.12 The x term is -0.2x. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2x + 0.01 + x2 = 0.12 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 0.12 + 0.01 Combine like terms: 0.12 + 0.01 = 0.13 0.01 + -0.2x + x2 = 0.13 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 0.13 Calculate the square root of the right side: 0.360555128 Break this problem into two subproblems by setting (x + -0.1) equal to 0.360555128 and -0.360555128.Subproblem 1
x + -0.1 = 0.360555128 Simplifying x + -0.1 = 0.360555128 Reorder the terms: -0.1 + x = 0.360555128 Solving -0.1 + x = 0.360555128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = 0.360555128 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 0.360555128 + 0.1 x = 0.360555128 + 0.1 Combine like terms: 0.360555128 + 0.1 = 0.460555128 x = 0.460555128 Simplifying x = 0.460555128Subproblem 2
x + -0.1 = -0.360555128 Simplifying x + -0.1 = -0.360555128 Reorder the terms: -0.1 + x = -0.360555128 Solving -0.1 + x = -0.360555128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = -0.360555128 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -0.360555128 + 0.1 x = -0.360555128 + 0.1 Combine like terms: -0.360555128 + 0.1 = -0.260555128 x = -0.260555128 Simplifying x = -0.260555128Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.460555128, -0.260555128}
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