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Simplifying 8x2 + -56x + 196 = 696 Reorder the terms: 196 + -56x + 8x2 = 696 Solving 196 + -56x + 8x2 = 696 Solving for variable 'x'. Reorder the terms: 196 + -696 + -56x + 8x2 = 696 + -696 Combine like terms: 196 + -696 = -500 -500 + -56x + 8x2 = 696 + -696 Combine like terms: 696 + -696 = 0 -500 + -56x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-125 + -14x + 2x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-125 + -14x + 2x2)' equal to zero and attempt to solve: Simplifying -125 + -14x + 2x2 = 0 Solving -125 + -14x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -62.5 + -7x + x2 = 0 Move the constant term to the right: Add '62.5' to each side of the equation. -62.5 + -7x + 62.5 + x2 = 0 + 62.5 Reorder the terms: -62.5 + 62.5 + -7x + x2 = 0 + 62.5 Combine like terms: -62.5 + 62.5 = 0.0 0.0 + -7x + x2 = 0 + 62.5 -7x + x2 = 0 + 62.5 Combine like terms: 0 + 62.5 = 62.5 -7x + x2 = 62.5 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 62.5 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 62.5 + 12.25 Combine like terms: 62.5 + 12.25 = 74.75 12.25 + -7x + x2 = 74.75 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 74.75 Calculate the square root of the right side: 8.645808233 Break this problem into two subproblems by setting (x + -3.5) equal to 8.645808233 and -8.645808233.Subproblem 1
x + -3.5 = 8.645808233 Simplifying x + -3.5 = 8.645808233 Reorder the terms: -3.5 + x = 8.645808233 Solving -3.5 + x = 8.645808233 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 8.645808233 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 8.645808233 + 3.5 x = 8.645808233 + 3.5 Combine like terms: 8.645808233 + 3.5 = 12.145808233 x = 12.145808233 Simplifying x = 12.145808233Subproblem 2
x + -3.5 = -8.645808233 Simplifying x + -3.5 = -8.645808233 Reorder the terms: -3.5 + x = -8.645808233 Solving -3.5 + x = -8.645808233 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -8.645808233 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -8.645808233 + 3.5 x = -8.645808233 + 3.5 Combine like terms: -8.645808233 + 3.5 = -5.145808233 x = -5.145808233 Simplifying x = -5.145808233Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.145808233, -5.145808233}Solution
x = {12.145808233, -5.145808233}
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