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Simplifying -2x + 41 = 5x2 + -10x + -210 Reorder the terms: 41 + -2x = 5x2 + -10x + -210 Reorder the terms: 41 + -2x = -210 + -10x + 5x2 Solving 41 + -2x = -210 + -10x + 5x2 Solving for variable 'x'. Reorder the terms: 41 + 210 + -2x + 10x + -5x2 = -210 + -10x + 5x2 + 210 + 10x + -5x2 Combine like terms: 41 + 210 = 251 251 + -2x + 10x + -5x2 = -210 + -10x + 5x2 + 210 + 10x + -5x2 Combine like terms: -2x + 10x = 8x 251 + 8x + -5x2 = -210 + -10x + 5x2 + 210 + 10x + -5x2 Reorder the terms: 251 + 8x + -5x2 = -210 + 210 + -10x + 10x + 5x2 + -5x2 Combine like terms: -210 + 210 = 0 251 + 8x + -5x2 = 0 + -10x + 10x + 5x2 + -5x2 251 + 8x + -5x2 = -10x + 10x + 5x2 + -5x2 Combine like terms: -10x + 10x = 0 251 + 8x + -5x2 = 0 + 5x2 + -5x2 251 + 8x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 251 + 8x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -50.2 + -1.6x + x2 = 0 Move the constant term to the right: Add '50.2' to each side of the equation. -50.2 + -1.6x + 50.2 + x2 = 0 + 50.2 Reorder the terms: -50.2 + 50.2 + -1.6x + x2 = 0 + 50.2 Combine like terms: -50.2 + 50.2 = 0.0 0.0 + -1.6x + x2 = 0 + 50.2 -1.6x + x2 = 0 + 50.2 Combine like terms: 0 + 50.2 = 50.2 -1.6x + x2 = 50.2 The x term is -1.6x. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6x + 0.64 + x2 = 50.2 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = 50.2 + 0.64 Combine like terms: 50.2 + 0.64 = 50.84 0.64 + -1.6x + x2 = 50.84 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 50.84 Calculate the square root of the right side: 7.130217388 Break this problem into two subproblems by setting (x + -0.8) equal to 7.130217388 and -7.130217388.Subproblem 1
x + -0.8 = 7.130217388 Simplifying x + -0.8 = 7.130217388 Reorder the terms: -0.8 + x = 7.130217388 Solving -0.8 + x = 7.130217388 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 7.130217388 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 7.130217388 + 0.8 x = 7.130217388 + 0.8 Combine like terms: 7.130217388 + 0.8 = 7.930217388 x = 7.930217388 Simplifying x = 7.930217388Subproblem 2
x + -0.8 = -7.130217388 Simplifying x + -0.8 = -7.130217388 Reorder the terms: -0.8 + x = -7.130217388 Solving -0.8 + x = -7.130217388 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = -7.130217388 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -7.130217388 + 0.8 x = -7.130217388 + 0.8 Combine like terms: -7.130217388 + 0.8 = -6.330217388 x = -6.330217388 Simplifying x = -6.330217388Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.930217388, -6.330217388}
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