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Simplifying x2 + -6x + -9 = 4.25 Reorder the terms: -9 + -6x + x2 = 4.25 Solving -9 + -6x + x2 = 4.25 Solving for variable 'x'. Reorder the terms: -9 + -4.25 + -6x + x2 = 4.25 + -4.25 Combine like terms: -9 + -4.25 = -13.25 -13.25 + -6x + x2 = 4.25 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 -13.25 + -6x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '13.25' to each side of the equation. -13.25 + -6x + 13.25 + x2 = 0.00 + 13.25 Reorder the terms: -13.25 + 13.25 + -6x + x2 = 0.00 + 13.25 Combine like terms: -13.25 + 13.25 = 0.00 0.00 + -6x + x2 = 0.00 + 13.25 -6x + x2 = 0.00 + 13.25 Combine like terms: 0.00 + 13.25 = 13.25 -6x + x2 = 13.25 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 13.25 + 9 Reorder the terms: 9 + -6x + x2 = 13.25 + 9 Combine like terms: 13.25 + 9 = 22.25 9 + -6x + x2 = 22.25 Factor a perfect square on the left side: (x + -3)(x + -3) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (x + -3) equal to 4.716990566 and -4.716990566.Subproblem 1
x + -3 = 4.716990566 Simplifying x + -3 = 4.716990566 Reorder the terms: -3 + x = 4.716990566 Solving -3 + x = 4.716990566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 4.716990566 + 3 Combine like terms: -3 + 3 = 0 0 + x = 4.716990566 + 3 x = 4.716990566 + 3 Combine like terms: 4.716990566 + 3 = 7.716990566 x = 7.716990566 Simplifying x = 7.716990566Subproblem 2
x + -3 = -4.716990566 Simplifying x + -3 = -4.716990566 Reorder the terms: -3 + x = -4.716990566 Solving -3 + x = -4.716990566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -4.716990566 + 3 Combine like terms: -3 + 3 = 0 0 + x = -4.716990566 + 3 x = -4.716990566 + 3 Combine like terms: -4.716990566 + 3 = -1.716990566 x = -1.716990566 Simplifying x = -1.716990566Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.716990566, -1.716990566}
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