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Simplifying x2 = 15 + 9x Solving x2 = 15 + 9x Solving for variable 'x'. Reorder the terms: -15 + -9x + x2 = 15 + 9x + -15 + -9x Reorder the terms: -15 + -9x + x2 = 15 + -15 + 9x + -9x Combine like terms: 15 + -15 = 0 -15 + -9x + x2 = 0 + 9x + -9x -15 + -9x + x2 = 9x + -9x Combine like terms: 9x + -9x = 0 -15 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + -9x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + -9x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -9x + x2 = 0 + 15 -9x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -9x + x2 = 15 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 15 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 15 + 20.25 Combine like terms: 15 + 20.25 = 35.25 20.25 + -9x + x2 = 35.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 35.25 Calculate the square root of the right side: 5.937171044 Break this problem into two subproblems by setting (x + -4.5) equal to 5.937171044 and -5.937171044.Subproblem 1
x + -4.5 = 5.937171044 Simplifying x + -4.5 = 5.937171044 Reorder the terms: -4.5 + x = 5.937171044 Solving -4.5 + x = 5.937171044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 5.937171044 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 5.937171044 + 4.5 x = 5.937171044 + 4.5 Combine like terms: 5.937171044 + 4.5 = 10.437171044 x = 10.437171044 Simplifying x = 10.437171044Subproblem 2
x + -4.5 = -5.937171044 Simplifying x + -4.5 = -5.937171044 Reorder the terms: -4.5 + x = -5.937171044 Solving -4.5 + x = -5.937171044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -5.937171044 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -5.937171044 + 4.5 x = -5.937171044 + 4.5 Combine like terms: -5.937171044 + 4.5 = -1.437171044 x = -1.437171044 Simplifying x = -1.437171044Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.437171044, -1.437171044}
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