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Simplifying 4x2 + 12x + -81 = 0 Reorder the terms: -81 + 12x + 4x2 = 0 Solving -81 + 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'. -20.25 + 3x + x2 = 0 Move the constant term to the right: Add '20.25' to each side of the equation. -20.25 + 3x + 20.25 + x2 = 0 + 20.25 Reorder the terms: -20.25 + 20.25 + 3x + x2 = 0 + 20.25 Combine like terms: -20.25 + 20.25 = 0.00 0.00 + 3x + x2 = 0 + 20.25 3x + x2 = 0 + 20.25 Combine like terms: 0 + 20.25 = 20.25 3x + x2 = 20.25 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 = 20.25 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 20.25 + 2.25 Combine like terms: 20.25 + 2.25 = 22.5 2.25 + 3x + x2 = 22.5 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 22.5 Calculate the square root of the right side: 4.74341649 Break this problem into two subproblems by setting (x + 1.5) equal to 4.74341649 and -4.74341649.Subproblem 1
x + 1.5 = 4.74341649 Simplifying x + 1.5 = 4.74341649 Reorder the terms: 1.5 + x = 4.74341649 Solving 1.5 + x = 4.74341649 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 = 4.74341649 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 4.74341649 + -1.5 x = 4.74341649 + -1.5 Combine like terms: 4.74341649 + -1.5 = 3.24341649 x = 3.24341649 Simplifying x = 3.24341649Subproblem 2
x + 1.5 = -4.74341649 Simplifying x + 1.5 = -4.74341649 Reorder the terms: 1.5 + x = -4.74341649 Solving 1.5 + x = -4.74341649 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 = -4.74341649 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -4.74341649 + -1.5 x = -4.74341649 + -1.5 Combine like terms: -4.74341649 + -1.5 = -6.24341649 x = -6.24341649 Simplifying x = -6.24341649Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.24341649, -6.24341649}
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