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Simplifying 3x2 + -1x2 + -12x + -9 = 0 Reorder the terms: -9 + -12x + 3x2 + -1x2 = 0 Combine like terms: 3x2 + -1x2 = 2x2 -9 + -12x + 2x2 = 0 Solving -9 + -12x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4.5 + -6x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -6x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -6x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -6x + x2 = 0 + 4.5 -6x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -6x + x2 = 4.5 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 = 4.5 + 9 Reorder the terms: 9 + -6x + x2 = 4.5 + 9 Combine like terms: 4.5 + 9 = 13.5 9 + -6x + x2 = 13.5 Factor a perfect square on the left side: (x + -3)(x + -3) = 13.5 Calculate the square root of the right side: 3.674234614 Break this problem into two subproblems by setting (x + -3) equal to 3.674234614 and -3.674234614.Subproblem 1
x + -3 = 3.674234614 Simplifying x + -3 = 3.674234614 Reorder the terms: -3 + x = 3.674234614 Solving -3 + x = 3.674234614 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 = 3.674234614 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.674234614 + 3 x = 3.674234614 + 3 Combine like terms: 3.674234614 + 3 = 6.674234614 x = 6.674234614 Simplifying x = 6.674234614Subproblem 2
x + -3 = -3.674234614 Simplifying x + -3 = -3.674234614 Reorder the terms: -3 + x = -3.674234614 Solving -3 + x = -3.674234614 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 = -3.674234614 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.674234614 + 3 x = -3.674234614 + 3 Combine like terms: -3.674234614 + 3 = -0.674234614 x = -0.674234614 Simplifying x = -0.674234614Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.674234614, -0.674234614}
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