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Simplifying 4x2 + -12x + -105 = 0 Reorder the terms: -105 + -12x + 4x2 = 0 Solving -105 + -12x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -26.25 + -3x + x2 = 0 Move the constant term to the right: Add '26.25' to each side of the equation. -26.25 + -3x + 26.25 + x2 = 0 + 26.25 Reorder the terms: -26.25 + 26.25 + -3x + x2 = 0 + 26.25 Combine like terms: -26.25 + 26.25 = 0.00 0.00 + -3x + x2 = 0 + 26.25 -3x + x2 = 0 + 26.25 Combine like terms: 0 + 26.25 = 26.25 -3x + x2 = 26.25 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 26.25 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 26.25 + 2.25 Combine like terms: 26.25 + 2.25 = 28.5 2.25 + -3x + x2 = 28.5 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 28.5 Calculate the square root of the right side: 5.338539126 Break this problem into two subproblems by setting (x + -1.5) equal to 5.338539126 and -5.338539126.Subproblem 1
x + -1.5 = 5.338539126 Simplifying x + -1.5 = 5.338539126 Reorder the terms: -1.5 + x = 5.338539126 Solving -1.5 + x = 5.338539126 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 5.338539126 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 5.338539126 + 1.5 x = 5.338539126 + 1.5 Combine like terms: 5.338539126 + 1.5 = 6.838539126 x = 6.838539126 Simplifying x = 6.838539126Subproblem 2
x + -1.5 = -5.338539126 Simplifying x + -1.5 = -5.338539126 Reorder the terms: -1.5 + x = -5.338539126 Solving -1.5 + x = -5.338539126 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -5.338539126 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -5.338539126 + 1.5 x = -5.338539126 + 1.5 Combine like terms: -5.338539126 + 1.5 = -3.838539126 x = -3.838539126 Simplifying x = -3.838539126Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.838539126, -3.838539126}
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