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Simplifying 4x2 + -6x + -39 = 0 Reorder the terms: -39 + -6x + 4x2 = 0 Solving -39 + -6x + 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'. -9.75 + -1.5x + x2 = 0 Move the constant term to the right: Add '9.75' to each side of the equation. -9.75 + -1.5x + 9.75 + x2 = 0 + 9.75 Reorder the terms: -9.75 + 9.75 + -1.5x + x2 = 0 + 9.75 Combine like terms: -9.75 + 9.75 = 0.00 0.00 + -1.5x + x2 = 0 + 9.75 -1.5x + x2 = 0 + 9.75 Combine like terms: 0 + 9.75 = 9.75 -1.5x + x2 = 9.75 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 9.75 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 9.75 + 0.5625 Combine like terms: 9.75 + 0.5625 = 10.3125 0.5625 + -1.5x + x2 = 10.3125 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 10.3125 Calculate the square root of the right side: 3.211308145 Break this problem into two subproblems by setting (x + -0.75) equal to 3.211308145 and -3.211308145.Subproblem 1
x + -0.75 = 3.211308145 Simplifying x + -0.75 = 3.211308145 Reorder the terms: -0.75 + x = 3.211308145 Solving -0.75 + x = 3.211308145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 3.211308145 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 3.211308145 + 0.75 x = 3.211308145 + 0.75 Combine like terms: 3.211308145 + 0.75 = 3.961308145 x = 3.961308145 Simplifying x = 3.961308145Subproblem 2
x + -0.75 = -3.211308145 Simplifying x + -0.75 = -3.211308145 Reorder the terms: -0.75 + x = -3.211308145 Solving -0.75 + x = -3.211308145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -3.211308145 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -3.211308145 + 0.75 x = -3.211308145 + 0.75 Combine like terms: -3.211308145 + 0.75 = -2.461308145 x = -2.461308145 Simplifying x = -2.461308145Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.961308145, -2.461308145}
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