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Simplifying x2 + -15x + -22 = 0 Reorder the terms: -22 + -15x + x2 = 0 Solving -22 + -15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + -15x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + -15x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + -15x + x2 = 0 + 22 -15x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 -15x + x2 = 22 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 = 22 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 22 + 56.25 Combine like terms: 22 + 56.25 = 78.25 56.25 + -15x + x2 = 78.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 78.25 Calculate the square root of the right side: 8.845903006 Break this problem into two subproblems by setting (x + -7.5) equal to 8.845903006 and -8.845903006.Subproblem 1
x + -7.5 = 8.845903006 Simplifying x + -7.5 = 8.845903006 Reorder the terms: -7.5 + x = 8.845903006 Solving -7.5 + x = 8.845903006 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 = 8.845903006 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 8.845903006 + 7.5 x = 8.845903006 + 7.5 Combine like terms: 8.845903006 + 7.5 = 16.345903006 x = 16.345903006 Simplifying x = 16.345903006Subproblem 2
x + -7.5 = -8.845903006 Simplifying x + -7.5 = -8.845903006 Reorder the terms: -7.5 + x = -8.845903006 Solving -7.5 + x = -8.845903006 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 = -8.845903006 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -8.845903006 + 7.5 x = -8.845903006 + 7.5 Combine like terms: -8.845903006 + 7.5 = -1.345903006 x = -1.345903006 Simplifying x = -1.345903006Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.345903006, -1.345903006}
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