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Simplifying 1[x] + [2x] + [2x(2x) + -5] = 2700 Remove parenthesis around (2x) 1x + [2x] + [2x * 2x + -5] = 2700 Reorder the terms for easier multiplication: 1x + [2x] + [2 * 2x * x + -5] = 2700 Multiply 2 * 2 1x + [2x] + [4x * x + -5] = 2700 Multiply x * x 1x + [2x] + [4x2 + -5] = 2700 Reorder the terms: 1x + [2x] + [-5 + 4x2] = 2700 Remove brackets around [-5 + 4x2] 1x + [2x] + -5 + 4x2 = 2700 Reorder the terms: -5 + 1x + [2x] + 4x2 = 2700 Combine like terms: 1x + [2x] = 3x -5 + 3x + 4x2 = 2700 Solving -5 + 3x + 4x2 = 2700 Solving for variable 'x'. Reorder the terms: -5 + -2700 + 3x + 4x2 = 2700 + -2700 Combine like terms: -5 + -2700 = -2705 -2705 + 3x + 4x2 = 2700 + -2700 Combine like terms: 2700 + -2700 = 0 -2705 + 3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -676.25 + 0.75x + x2 = 0 Move the constant term to the right: Add '676.25' to each side of the equation. -676.25 + 0.75x + 676.25 + x2 = 0 + 676.25 Reorder the terms: -676.25 + 676.25 + 0.75x + x2 = 0 + 676.25 Combine like terms: -676.25 + 676.25 = 0.00 0.00 + 0.75x + x2 = 0 + 676.25 0.75x + x2 = 0 + 676.25 Combine like terms: 0 + 676.25 = 676.25 0.75x + x2 = 676.25 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 676.25 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 676.25 + 0.140625 Combine like terms: 676.25 + 0.140625 = 676.390625 0.140625 + 0.75x + x2 = 676.390625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 676.390625 Calculate the square root of the right side: 26.007510934 Break this problem into two subproblems by setting (x + 0.375) equal to 26.007510934 and -26.007510934.Subproblem 1
x + 0.375 = 26.007510934 Simplifying x + 0.375 = 26.007510934 Reorder the terms: 0.375 + x = 26.007510934 Solving 0.375 + x = 26.007510934 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 26.007510934 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 26.007510934 + -0.375 x = 26.007510934 + -0.375 Combine like terms: 26.007510934 + -0.375 = 25.632510934 x = 25.632510934 Simplifying x = 25.632510934Subproblem 2
x + 0.375 = -26.007510934 Simplifying x + 0.375 = -26.007510934 Reorder the terms: 0.375 + x = -26.007510934 Solving 0.375 + x = -26.007510934 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -26.007510934 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -26.007510934 + -0.375 x = -26.007510934 + -0.375 Combine like terms: -26.007510934 + -0.375 = -26.382510934 x = -26.382510934 Simplifying x = -26.382510934Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.632510934, -26.382510934}
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