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Simplifying 2x + -1x * x + 8 * 2x + 5x + -3 = 0 Multiply x * x 2x + -1x2 + 8 * 2x + 5x + -3 = 0 Multiply 8 * 2 2x + -1x2 + 16x + 5x + -3 = 0 Reorder the terms: -3 + 2x + 16x + 5x + -1x2 = 0 Combine like terms: 2x + 16x = 18x -3 + 18x + 5x + -1x2 = 0 Combine like terms: 18x + 5x = 23x -3 + 23x + -1x2 = 0 Solving -3 + 23x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 3 + -23x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -23x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -23x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -23x + x2 = 0 + -3 -23x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -23x + x2 = -3 The x term is -23x. Take half its coefficient (-11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. -23x + 132.25 + x2 = -3 + 132.25 Reorder the terms: 132.25 + -23x + x2 = -3 + 132.25 Combine like terms: -3 + 132.25 = 129.25 132.25 + -23x + x2 = 129.25 Factor a perfect square on the left side: (x + -11.5)(x + -11.5) = 129.25 Calculate the square root of the right side: 11.368817001 Break this problem into two subproblems by setting (x + -11.5) equal to 11.368817001 and -11.368817001.Subproblem 1
x + -11.5 = 11.368817001 Simplifying x + -11.5 = 11.368817001 Reorder the terms: -11.5 + x = 11.368817001 Solving -11.5 + x = 11.368817001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = 11.368817001 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 11.368817001 + 11.5 x = 11.368817001 + 11.5 Combine like terms: 11.368817001 + 11.5 = 22.868817001 x = 22.868817001 Simplifying x = 22.868817001Subproblem 2
x + -11.5 = -11.368817001 Simplifying x + -11.5 = -11.368817001 Reorder the terms: -11.5 + x = -11.368817001 Solving -11.5 + x = -11.368817001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = -11.368817001 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -11.368817001 + 11.5 x = -11.368817001 + 11.5 Combine like terms: -11.368817001 + 11.5 = 0.131182999 x = 0.131182999 Simplifying x = 0.131182999Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.868817001, 0.131182999}
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