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Simplifying 4x2 + 12x + -49 = 0 Reorder the terms: -49 + 12x + 4x2 = 0 Solving -49 + 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'. -12.25 + 3x + x2 = 0 Move the constant term to the right: Add '12.25' to each side of the equation. -12.25 + 3x + 12.25 + x2 = 0 + 12.25 Reorder the terms: -12.25 + 12.25 + 3x + x2 = 0 + 12.25 Combine like terms: -12.25 + 12.25 = 0.00 0.00 + 3x + x2 = 0 + 12.25 3x + x2 = 0 + 12.25 Combine like terms: 0 + 12.25 = 12.25 3x + x2 = 12.25 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 = 12.25 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 12.25 + 2.25 Combine like terms: 12.25 + 2.25 = 14.5 2.25 + 3x + x2 = 14.5 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 14.5 Calculate the square root of the right side: 3.807886553 Break this problem into two subproblems by setting (x + 1.5) equal to 3.807886553 and -3.807886553.Subproblem 1
x + 1.5 = 3.807886553 Simplifying x + 1.5 = 3.807886553 Reorder the terms: 1.5 + x = 3.807886553 Solving 1.5 + x = 3.807886553 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 = 3.807886553 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 3.807886553 + -1.5 x = 3.807886553 + -1.5 Combine like terms: 3.807886553 + -1.5 = 2.307886553 x = 2.307886553 Simplifying x = 2.307886553Subproblem 2
x + 1.5 = -3.807886553 Simplifying x + 1.5 = -3.807886553 Reorder the terms: 1.5 + x = -3.807886553 Solving 1.5 + x = -3.807886553 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 = -3.807886553 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -3.807886553 + -1.5 x = -3.807886553 + -1.5 Combine like terms: -3.807886553 + -1.5 = -5.307886553 x = -5.307886553 Simplifying x = -5.307886553Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.307886553, -5.307886553}
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