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Simplifying x2 + -6x + 9 = 149 Reorder the terms: 9 + -6x + x2 = 149 Solving 9 + -6x + x2 = 149 Solving for variable 'x'. Reorder the terms: 9 + -149 + -6x + x2 = 149 + -149 Combine like terms: 9 + -149 = -140 -140 + -6x + x2 = 149 + -149 Combine like terms: 149 + -149 = 0 -140 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '140' to each side of the equation. -140 + -6x + 140 + x2 = 0 + 140 Reorder the terms: -140 + 140 + -6x + x2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + -6x + x2 = 0 + 140 -6x + x2 = 0 + 140 Combine like terms: 0 + 140 = 140 -6x + x2 = 140 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 = 140 + 9 Reorder the terms: 9 + -6x + x2 = 140 + 9 Combine like terms: 140 + 9 = 149 9 + -6x + x2 = 149 Factor a perfect square on the left side: (x + -3)(x + -3) = 149 Calculate the square root of the right side: 12.206555616 Break this problem into two subproblems by setting (x + -3) equal to 12.206555616 and -12.206555616.Subproblem 1
x + -3 = 12.206555616 Simplifying x + -3 = 12.206555616 Reorder the terms: -3 + x = 12.206555616 Solving -3 + x = 12.206555616 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 = 12.206555616 + 3 Combine like terms: -3 + 3 = 0 0 + x = 12.206555616 + 3 x = 12.206555616 + 3 Combine like terms: 12.206555616 + 3 = 15.206555616 x = 15.206555616 Simplifying x = 15.206555616Subproblem 2
x + -3 = -12.206555616 Simplifying x + -3 = -12.206555616 Reorder the terms: -3 + x = -12.206555616 Solving -3 + x = -12.206555616 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 = -12.206555616 + 3 Combine like terms: -3 + 3 = 0 0 + x = -12.206555616 + 3 x = -12.206555616 + 3 Combine like terms: -12.206555616 + 3 = -9.206555616 x = -9.206555616 Simplifying x = -9.206555616Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.206555616, -9.206555616}
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