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Simplifying 2x2 + 3x + 500 = 3x2 + x + 300 Reorder the terms: 500 + 3x + 2x2 = 3x2 + x + 300 Reorder the terms: 500 + 3x + 2x2 = 300 + x + 3x2 Solving 500 + 3x + 2x2 = 300 + x + 3x2 Solving for variable 'x'. Reorder the terms: 500 + -300 + 3x + -1x + 2x2 + -3x2 = 300 + x + 3x2 + -300 + -1x + -3x2 Combine like terms: 500 + -300 = 200 200 + 3x + -1x + 2x2 + -3x2 = 300 + x + 3x2 + -300 + -1x + -3x2 Combine like terms: 3x + -1x = 2x 200 + 2x + 2x2 + -3x2 = 300 + x + 3x2 + -300 + -1x + -3x2 Combine like terms: 2x2 + -3x2 = -1x2 200 + 2x + -1x2 = 300 + x + 3x2 + -300 + -1x + -3x2 Reorder the terms: 200 + 2x + -1x2 = 300 + -300 + x + -1x + 3x2 + -3x2 Combine like terms: 300 + -300 = 0 200 + 2x + -1x2 = 0 + x + -1x + 3x2 + -3x2 200 + 2x + -1x2 = x + -1x + 3x2 + -3x2 Combine like terms: x + -1x = 0 200 + 2x + -1x2 = 0 + 3x2 + -3x2 200 + 2x + -1x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 200 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -200 + -2x + x2 = 0 Move the constant term to the right: Add '200' to each side of the equation. -200 + -2x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + -2x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + -2x + x2 = 0 + 200 -2x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 -2x + x2 = 200 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 200 + 1 Reorder the terms: 1 + -2x + x2 = 200 + 1 Combine like terms: 200 + 1 = 201 1 + -2x + x2 = 201 Factor a perfect square on the left side: (x + -1)(x + -1) = 201 Calculate the square root of the right side: 14.177446879 Break this problem into two subproblems by setting (x + -1) equal to 14.177446879 and -14.177446879.Subproblem 1
x + -1 = 14.177446879 Simplifying x + -1 = 14.177446879 Reorder the terms: -1 + x = 14.177446879 Solving -1 + x = 14.177446879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 14.177446879 + 1 Combine like terms: -1 + 1 = 0 0 + x = 14.177446879 + 1 x = 14.177446879 + 1 Combine like terms: 14.177446879 + 1 = 15.177446879 x = 15.177446879 Simplifying x = 15.177446879Subproblem 2
x + -1 = -14.177446879 Simplifying x + -1 = -14.177446879 Reorder the terms: -1 + x = -14.177446879 Solving -1 + x = -14.177446879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -14.177446879 + 1 Combine like terms: -1 + 1 = 0 0 + x = -14.177446879 + 1 x = -14.177446879 + 1 Combine like terms: -14.177446879 + 1 = -13.177446879 x = -13.177446879 Simplifying x = -13.177446879Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.177446879, -13.177446879}
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