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Simplifying 4x2 + 12x + -224 = 0 Reorder the terms: -224 + 12x + 4x2 = 0 Solving -224 + 12x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-56 + 3x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-56 + 3x + x2)' equal to zero and attempt to solve: Simplifying -56 + 3x + x2 = 0 Solving -56 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + 3x + 56 + x2 = 0 + 56 Reorder the terms: -56 + 56 + 3x + x2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + 3x + x2 = 0 + 56 3x + x2 = 0 + 56 Combine like terms: 0 + 56 = 56 3x + x2 = 56 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 = 56 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 56 + 2.25 Combine like terms: 56 + 2.25 = 58.25 2.25 + 3x + x2 = 58.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 58.25 Calculate the square root of the right side: 7.632168761 Break this problem into two subproblems by setting (x + 1.5) equal to 7.632168761 and -7.632168761.Subproblem 1
x + 1.5 = 7.632168761 Simplifying x + 1.5 = 7.632168761 Reorder the terms: 1.5 + x = 7.632168761 Solving 1.5 + x = 7.632168761 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 = 7.632168761 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 7.632168761 + -1.5 x = 7.632168761 + -1.5 Combine like terms: 7.632168761 + -1.5 = 6.132168761 x = 6.132168761 Simplifying x = 6.132168761Subproblem 2
x + 1.5 = -7.632168761 Simplifying x + 1.5 = -7.632168761 Reorder the terms: 1.5 + x = -7.632168761 Solving 1.5 + x = -7.632168761 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 = -7.632168761 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -7.632168761 + -1.5 x = -7.632168761 + -1.5 Combine like terms: -7.632168761 + -1.5 = -9.132168761 x = -9.132168761 Simplifying x = -9.132168761Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.132168761, -9.132168761}Solution
x = {6.132168761, -9.132168761}
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