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Simplifying 4x2 + 12x + -784 = 0 Reorder the terms: -784 + 12x + 4x2 = 0 Solving -784 + 12x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-196 + 3x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-196 + 3x + x2)' equal to zero and attempt to solve: Simplifying -196 + 3x + x2 = 0 Solving -196 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '196' to each side of the equation. -196 + 3x + 196 + x2 = 0 + 196 Reorder the terms: -196 + 196 + 3x + x2 = 0 + 196 Combine like terms: -196 + 196 = 0 0 + 3x + x2 = 0 + 196 3x + x2 = 0 + 196 Combine like terms: 0 + 196 = 196 3x + x2 = 196 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 = 196 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 196 + 2.25 Combine like terms: 196 + 2.25 = 198.25 2.25 + 3x + x2 = 198.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 198.25 Calculate the square root of the right side: 14.08012784 Break this problem into two subproblems by setting (x + 1.5) equal to 14.08012784 and -14.08012784.Subproblem 1
x + 1.5 = 14.08012784 Simplifying x + 1.5 = 14.08012784 Reorder the terms: 1.5 + x = 14.08012784 Solving 1.5 + x = 14.08012784 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 = 14.08012784 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 14.08012784 + -1.5 x = 14.08012784 + -1.5 Combine like terms: 14.08012784 + -1.5 = 12.58012784 x = 12.58012784 Simplifying x = 12.58012784Subproblem 2
x + 1.5 = -14.08012784 Simplifying x + 1.5 = -14.08012784 Reorder the terms: 1.5 + x = -14.08012784 Solving 1.5 + x = -14.08012784 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 = -14.08012784 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -14.08012784 + -1.5 x = -14.08012784 + -1.5 Combine like terms: -14.08012784 + -1.5 = -15.58012784 x = -15.58012784 Simplifying x = -15.58012784Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.58012784, -15.58012784}Solution
x = {12.58012784, -15.58012784}
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