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Simplifying 51 * 27x2 = x + 17 Multiply 51 * 27 1377x2 = x + 17 Reorder the terms: 1377x2 = 17 + x Solving 1377x2 = 17 + x Solving for variable 'x'. Reorder the terms: -17 + -1x + 1377x2 = 17 + x + -17 + -1x Reorder the terms: -17 + -1x + 1377x2 = 17 + -17 + x + -1x Combine like terms: 17 + -17 = 0 -17 + -1x + 1377x2 = 0 + x + -1x -17 + -1x + 1377x2 = x + -1x Combine like terms: x + -1x = 0 -17 + -1x + 1377x2 = 0 Begin completing the square. Divide all terms by 1377 the coefficient of the squared term: Divide each side by '1377'. -0.01234567901 + -0.0007262164125x + x2 = 0 Move the constant term to the right: Add '0.01234567901' to each side of the equation. -0.01234567901 + -0.0007262164125x + 0.01234567901 + x2 = 0 + 0.01234567901 Reorder the terms: -0.01234567901 + 0.01234567901 + -0.0007262164125x + x2 = 0 + 0.01234567901 Combine like terms: -0.01234567901 + 0.01234567901 = 0.00000000000 0.00000000000 + -0.0007262164125x + x2 = 0 + 0.01234567901 -0.0007262164125x + x2 = 0 + 0.01234567901 Combine like terms: 0 + 0.01234567901 = 0.01234567901 -0.0007262164125x + x2 = 0.01234567901 The x term is -0.0007262164125x. Take half its coefficient (-0.0003631082063). Square it (0.0000001318475695) and add it to both sides. Add '0.0000001318475695' to each side of the equation. -0.0007262164125x + 0.0000001318475695 + x2 = 0.01234567901 + 0.0000001318475695 Reorder the terms: 0.0000001318475695 + -0.0007262164125x + x2 = 0.01234567901 + 0.0000001318475695 Combine like terms: 0.01234567901 + 0.0000001318475695 = 0.0123458108575695 0.0000001318475695 + -0.0007262164125x + x2 = 0.0123458108575695 Factor a perfect square on the left side: (x + -0.0003631082063)(x + -0.0003631082063) = 0.0123458108575695 Calculate the square root of the right side: 0.111111704 Break this problem into two subproblems by setting (x + -0.0003631082063) equal to 0.111111704 and -0.111111704.Subproblem 1
x + -0.0003631082063 = 0.111111704 Simplifying x + -0.0003631082063 = 0.111111704 Reorder the terms: -0.0003631082063 + x = 0.111111704 Solving -0.0003631082063 + x = 0.111111704 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0003631082063' to each side of the equation. -0.0003631082063 + 0.0003631082063 + x = 0.111111704 + 0.0003631082063 Combine like terms: -0.0003631082063 + 0.0003631082063 = 0.0000000000000 0.0000000000000 + x = 0.111111704 + 0.0003631082063 x = 0.111111704 + 0.0003631082063 Combine like terms: 0.111111704 + 0.0003631082063 = 0.1114748122063 x = 0.1114748122063 Simplifying x = 0.1114748122063Subproblem 2
x + -0.0003631082063 = -0.111111704 Simplifying x + -0.0003631082063 = -0.111111704 Reorder the terms: -0.0003631082063 + x = -0.111111704 Solving -0.0003631082063 + x = -0.111111704 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0003631082063' to each side of the equation. -0.0003631082063 + 0.0003631082063 + x = -0.111111704 + 0.0003631082063 Combine like terms: -0.0003631082063 + 0.0003631082063 = 0.0000000000000 0.0000000000000 + x = -0.111111704 + 0.0003631082063 x = -0.111111704 + 0.0003631082063 Combine like terms: -0.111111704 + 0.0003631082063 = -0.1107485957937 x = -0.1107485957937 Simplifying x = -0.1107485957937Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1114748122063, -0.1107485957937}
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