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Simplifying x = 5x2 + -40x + -27 Reorder the terms: x = -27 + -40x + 5x2 Solving x = -27 + -40x + 5x2 Solving for variable 'x'. Reorder the terms: 27 + x + 40x + -5x2 = -27 + -40x + 5x2 + 27 + 40x + -5x2 Combine like terms: x + 40x = 41x 27 + 41x + -5x2 = -27 + -40x + 5x2 + 27 + 40x + -5x2 Reorder the terms: 27 + 41x + -5x2 = -27 + 27 + -40x + 40x + 5x2 + -5x2 Combine like terms: -27 + 27 = 0 27 + 41x + -5x2 = 0 + -40x + 40x + 5x2 + -5x2 27 + 41x + -5x2 = -40x + 40x + 5x2 + -5x2 Combine like terms: -40x + 40x = 0 27 + 41x + -5x2 = 0 + 5x2 + -5x2 27 + 41x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 27 + 41x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -5.4 + -8.2x + x2 = 0 Move the constant term to the right: Add '5.4' to each side of the equation. -5.4 + -8.2x + 5.4 + x2 = 0 + 5.4 Reorder the terms: -5.4 + 5.4 + -8.2x + x2 = 0 + 5.4 Combine like terms: -5.4 + 5.4 = 0.0 0.0 + -8.2x + x2 = 0 + 5.4 -8.2x + x2 = 0 + 5.4 Combine like terms: 0 + 5.4 = 5.4 -8.2x + x2 = 5.4 The x term is -8.2x. Take half its coefficient (-4.1). Square it (16.81) and add it to both sides. Add '16.81' to each side of the equation. -8.2x + 16.81 + x2 = 5.4 + 16.81 Reorder the terms: 16.81 + -8.2x + x2 = 5.4 + 16.81 Combine like terms: 5.4 + 16.81 = 22.21 16.81 + -8.2x + x2 = 22.21 Factor a perfect square on the left side: (x + -4.1)(x + -4.1) = 22.21 Calculate the square root of the right side: 4.712748667 Break this problem into two subproblems by setting (x + -4.1) equal to 4.712748667 and -4.712748667.Subproblem 1
x + -4.1 = 4.712748667 Simplifying x + -4.1 = 4.712748667 Reorder the terms: -4.1 + x = 4.712748667 Solving -4.1 + x = 4.712748667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.1' to each side of the equation. -4.1 + 4.1 + x = 4.712748667 + 4.1 Combine like terms: -4.1 + 4.1 = 0.0 0.0 + x = 4.712748667 + 4.1 x = 4.712748667 + 4.1 Combine like terms: 4.712748667 + 4.1 = 8.812748667 x = 8.812748667 Simplifying x = 8.812748667Subproblem 2
x + -4.1 = -4.712748667 Simplifying x + -4.1 = -4.712748667 Reorder the terms: -4.1 + x = -4.712748667 Solving -4.1 + x = -4.712748667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.1' to each side of the equation. -4.1 + 4.1 + x = -4.712748667 + 4.1 Combine like terms: -4.1 + 4.1 = 0.0 0.0 + x = -4.712748667 + 4.1 x = -4.712748667 + 4.1 Combine like terms: -4.712748667 + 4.1 = -0.612748667 x = -0.612748667 Simplifying x = -0.612748667Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.812748667, -0.612748667}
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