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Simplifying 4x2 + 12x + -19 = 0 Reorder the terms: -19 + 12x + 4x2 = 0 Solving -19 + 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'. -4.75 + 3x + x2 = 0 Move the constant term to the right: Add '4.75' to each side of the equation. -4.75 + 3x + 4.75 + x2 = 0 + 4.75 Reorder the terms: -4.75 + 4.75 + 3x + x2 = 0 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + 3x + x2 = 0 + 4.75 3x + x2 = 0 + 4.75 Combine like terms: 0 + 4.75 = 4.75 3x + x2 = 4.75 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 = 4.75 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 4.75 + 2.25 Combine like terms: 4.75 + 2.25 = 7 2.25 + 3x + x2 = 7 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + 1.5) equal to 2.645751311 and -2.645751311.Subproblem 1
x + 1.5 = 2.645751311 Simplifying x + 1.5 = 2.645751311 Reorder the terms: 1.5 + x = 2.645751311 Solving 1.5 + x = 2.645751311 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 = 2.645751311 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.645751311 + -1.5 x = 2.645751311 + -1.5 Combine like terms: 2.645751311 + -1.5 = 1.145751311 x = 1.145751311 Simplifying x = 1.145751311Subproblem 2
x + 1.5 = -2.645751311 Simplifying x + 1.5 = -2.645751311 Reorder the terms: 1.5 + x = -2.645751311 Solving 1.5 + x = -2.645751311 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 = -2.645751311 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.645751311 + -1.5 x = -2.645751311 + -1.5 Combine like terms: -2.645751311 + -1.5 = -4.145751311 x = -4.145751311 Simplifying x = -4.145751311Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.145751311, -4.145751311}
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