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Simplifying 28x2 + 56x + -3920 = 0 Reorder the terms: -3920 + 56x + 28x2 = 0 Solving -3920 + 56x + 28x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '28'. 28(-140 + 2x + x2) = 0 Ignore the factor 28.Subproblem 1
Set the factor '(-140 + 2x + x2)' equal to zero and attempt to solve: Simplifying -140 + 2x + x2 = 0 Solving -140 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '140' to each side of the equation. -140 + 2x + 140 + x2 = 0 + 140 Reorder the terms: -140 + 140 + 2x + x2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + 2x + x2 = 0 + 140 2x + x2 = 0 + 140 Combine like terms: 0 + 140 = 140 2x + x2 = 140 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 140 + 1 Reorder the terms: 1 + 2x + x2 = 140 + 1 Combine like terms: 140 + 1 = 141 1 + 2x + x2 = 141 Factor a perfect square on the left side: (x + 1)(x + 1) = 141 Calculate the square root of the right side: 11.874342087 Break this problem into two subproblems by setting (x + 1) equal to 11.874342087 and -11.874342087.Subproblem 1
x + 1 = 11.874342087 Simplifying x + 1 = 11.874342087 Reorder the terms: 1 + x = 11.874342087 Solving 1 + x = 11.874342087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 11.874342087 + -1 Combine like terms: 1 + -1 = 0 0 + x = 11.874342087 + -1 x = 11.874342087 + -1 Combine like terms: 11.874342087 + -1 = 10.874342087 x = 10.874342087 Simplifying x = 10.874342087Subproblem 2
x + 1 = -11.874342087 Simplifying x + 1 = -11.874342087 Reorder the terms: 1 + x = -11.874342087 Solving 1 + x = -11.874342087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -11.874342087 + -1 Combine like terms: 1 + -1 = 0 0 + x = -11.874342087 + -1 x = -11.874342087 + -1 Combine like terms: -11.874342087 + -1 = -12.874342087 x = -12.874342087 Simplifying x = -12.874342087Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.874342087, -12.874342087}Solution
x = {10.874342087, -12.874342087}
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