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Simplifying x2 + 6x + 9x = 25 Reorder the terms: 6x + 9x + x2 = 25 Combine like terms: 6x + 9x = 15x 15x + x2 = 25 Solving 15x + x2 = 25 Solving for variable 'x'. Reorder the terms: -25 + 15x + x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 15x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + 15x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 15x + x2 = 0 + 25 15x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 15x + x2 = 25 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 = 25 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 25 + 56.25 Combine like terms: 25 + 56.25 = 81.25 56.25 + 15x + x2 = 81.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 81.25 Calculate the square root of the right side: 9.013878189 Break this problem into two subproblems by setting (x + 7.5) equal to 9.013878189 and -9.013878189.Subproblem 1
x + 7.5 = 9.013878189 Simplifying x + 7.5 = 9.013878189 Reorder the terms: 7.5 + x = 9.013878189 Solving 7.5 + x = 9.013878189 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 = 9.013878189 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 9.013878189 + -7.5 x = 9.013878189 + -7.5 Combine like terms: 9.013878189 + -7.5 = 1.513878189 x = 1.513878189 Simplifying x = 1.513878189Subproblem 2
x + 7.5 = -9.013878189 Simplifying x + 7.5 = -9.013878189 Reorder the terms: 7.5 + x = -9.013878189 Solving 7.5 + x = -9.013878189 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 = -9.013878189 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -9.013878189 + -7.5 x = -9.013878189 + -7.5 Combine like terms: -9.013878189 + -7.5 = -16.513878189 x = -16.513878189 Simplifying x = -16.513878189Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.513878189, -16.513878189}
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