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Simplifying 4x2 + 12x + -39 = 0 Reorder the terms: -39 + 12x + 4x2 = 0 Solving -39 + 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'. -9.75 + 3x + x2 = 0 Move the constant term to the right: Add '9.75' to each side of the equation. -9.75 + 3x + 9.75 + x2 = 0 + 9.75 Reorder the terms: -9.75 + 9.75 + 3x + x2 = 0 + 9.75 Combine like terms: -9.75 + 9.75 = 0.00 0.00 + 3x + x2 = 0 + 9.75 3x + x2 = 0 + 9.75 Combine like terms: 0 + 9.75 = 9.75 3x + x2 = 9.75 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 = 9.75 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 9.75 + 2.25 Combine like terms: 9.75 + 2.25 = 12 2.25 + 3x + x2 = 12 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x + 1.5) equal to 3.464101615 and -3.464101615.Subproblem 1
x + 1.5 = 3.464101615 Simplifying x + 1.5 = 3.464101615 Reorder the terms: 1.5 + x = 3.464101615 Solving 1.5 + x = 3.464101615 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 = 3.464101615 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 3.464101615 + -1.5 x = 3.464101615 + -1.5 Combine like terms: 3.464101615 + -1.5 = 1.964101615 x = 1.964101615 Simplifying x = 1.964101615Subproblem 2
x + 1.5 = -3.464101615 Simplifying x + 1.5 = -3.464101615 Reorder the terms: 1.5 + x = -3.464101615 Solving 1.5 + x = -3.464101615 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 = -3.464101615 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -3.464101615 + -1.5 x = -3.464101615 + -1.5 Combine like terms: -3.464101615 + -1.5 = -4.964101615 x = -4.964101615 Simplifying x = -4.964101615Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.964101615, -4.964101615}
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