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Simplifying 15x + x2 + -29 = 0 Reorder the terms: -29 + 15x + x2 = 0 Solving -29 + 15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + 15x + 29 + x2 = 0 + 29 Reorder the terms: -29 + 29 + 15x + x2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 15x + x2 = 0 + 29 15x + x2 = 0 + 29 Combine like terms: 0 + 29 = 29 15x + x2 = 29 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 29 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 29 + 56.25 Combine like terms: 29 + 56.25 = 85.25 56.25 + 15x + x2 = 85.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 85.25 Calculate the square root of the right side: 9.233092656 Break this problem into two subproblems by setting (x + 7.5) equal to 9.233092656 and -9.233092656.Subproblem 1
x + 7.5 = 9.233092656 Simplifying x + 7.5 = 9.233092656 Reorder the terms: 7.5 + x = 9.233092656 Solving 7.5 + x = 9.233092656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 9.233092656 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 9.233092656 + -7.5 x = 9.233092656 + -7.5 Combine like terms: 9.233092656 + -7.5 = 1.733092656 x = 1.733092656 Simplifying x = 1.733092656Subproblem 2
x + 7.5 = -9.233092656 Simplifying x + 7.5 = -9.233092656 Reorder the terms: 7.5 + x = -9.233092656 Solving 7.5 + x = -9.233092656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -9.233092656 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -9.233092656 + -7.5 x = -9.233092656 + -7.5 Combine like terms: -9.233092656 + -7.5 = -16.733092656 x = -16.733092656 Simplifying x = -16.733092656Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.733092656, -16.733092656}
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