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Simplifying 7x2 + -7x + -196 = 0 Reorder the terms: -196 + -7x + 7x2 = 0 Solving -196 + -7x + 7x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '7'. 7(-28 + -1x + x2) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-28 + -1x + x2)' equal to zero and attempt to solve: Simplifying -28 + -1x + x2 = 0 Solving -28 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + -1x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + -1x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -1x + x2 = 0 + 28 -1x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 -1x + x2 = 28 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 28 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 28 + 0.25 Combine like terms: 28 + 0.25 = 28.25 0.25 + -1x + x2 = 28.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (x + -0.5) equal to 5.315072906 and -5.315072906.Subproblem 1
x + -0.5 = 5.315072906 Simplifying x + -0.5 = 5.315072906 Reorder the terms: -0.5 + x = 5.315072906 Solving -0.5 + x = 5.315072906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 5.315072906 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 5.315072906 + 0.5 x = 5.315072906 + 0.5 Combine like terms: 5.315072906 + 0.5 = 5.815072906 x = 5.815072906 Simplifying x = 5.815072906Subproblem 2
x + -0.5 = -5.315072906 Simplifying x + -0.5 = -5.315072906 Reorder the terms: -0.5 + x = -5.315072906 Solving -0.5 + x = -5.315072906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -5.315072906 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -5.315072906 + 0.5 x = -5.315072906 + 0.5 Combine like terms: -5.315072906 + 0.5 = -4.815072906 x = -4.815072906 Simplifying x = -4.815072906Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.815072906, -4.815072906}Solution
x = {5.815072906, -4.815072906}
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