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Simplifying 80 = (20 + -2x)(8 + -2x) Multiply (20 + -2x) * (8 + -2x) 80 = (20(8 + -2x) + -2x * (8 + -2x)) 80 = ((8 * 20 + -2x * 20) + -2x * (8 + -2x)) 80 = ((160 + -40x) + -2x * (8 + -2x)) 80 = (160 + -40x + (8 * -2x + -2x * -2x)) 80 = (160 + -40x + (-16x + 4x2)) Combine like terms: -40x + -16x = -56x 80 = (160 + -56x + 4x2) Solving 80 = 160 + -56x + 4x2 Solving for variable 'x'. Combine like terms: 80 + -160 = -80 -80 + 56x + -4x2 = 160 + -56x + 4x2 + -160 + 56x + -4x2 Reorder the terms: -80 + 56x + -4x2 = 160 + -160 + -56x + 56x + 4x2 + -4x2 Combine like terms: 160 + -160 = 0 -80 + 56x + -4x2 = 0 + -56x + 56x + 4x2 + -4x2 -80 + 56x + -4x2 = -56x + 56x + 4x2 + -4x2 Combine like terms: -56x + 56x = 0 -80 + 56x + -4x2 = 0 + 4x2 + -4x2 -80 + 56x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -80 + 56x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-20 + 14x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-20 + 14x + -1x2)' equal to zero and attempt to solve: Simplifying -20 + 14x + -1x2 = 0 Solving -20 + 14x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 20 + -14x + x2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + -14x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + -14x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -14x + x2 = 0 + -20 -14x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 -14x + x2 = -20 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = -20 + 49 Reorder the terms: 49 + -14x + x2 = -20 + 49 Combine like terms: -20 + 49 = 29 49 + -14x + x2 = 29 Factor a perfect square on the left side: (x + -7)(x + -7) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (x + -7) equal to 5.385164807 and -5.385164807.Subproblem 1
x + -7 = 5.385164807 Simplifying x + -7 = 5.385164807 Reorder the terms: -7 + x = 5.385164807 Solving -7 + x = 5.385164807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 5.385164807 + 7 Combine like terms: -7 + 7 = 0 0 + x = 5.385164807 + 7 x = 5.385164807 + 7 Combine like terms: 5.385164807 + 7 = 12.385164807 x = 12.385164807 Simplifying x = 12.385164807Subproblem 2
x + -7 = -5.385164807 Simplifying x + -7 = -5.385164807 Reorder the terms: -7 + x = -5.385164807 Solving -7 + x = -5.385164807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -5.385164807 + 7 Combine like terms: -7 + 7 = 0 0 + x = -5.385164807 + 7 x = -5.385164807 + 7 Combine like terms: -5.385164807 + 7 = 1.614835193 x = 1.614835193 Simplifying x = 1.614835193Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.385164807, 1.614835193}Solution
x = {12.385164807, 1.614835193}
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