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Simplifying (2x + -40)(13x + -13) = 26 Reorder the terms: (-40 + 2x)(13x + -13) = 26 Reorder the terms: (-40 + 2x)(-13 + 13x) = 26 Multiply (-40 + 2x) * (-13 + 13x) (-40(-13 + 13x) + 2x * (-13 + 13x)) = 26 ((-13 * -40 + 13x * -40) + 2x * (-13 + 13x)) = 26 ((520 + -520x) + 2x * (-13 + 13x)) = 26 (520 + -520x + (-13 * 2x + 13x * 2x)) = 26 (520 + -520x + (-26x + 26x2)) = 26 Combine like terms: -520x + -26x = -546x (520 + -546x + 26x2) = 26 Solving 520 + -546x + 26x2 = 26 Solving for variable 'x'. Reorder the terms: 520 + -26 + -546x + 26x2 = 26 + -26 Combine like terms: 520 + -26 = 494 494 + -546x + 26x2 = 26 + -26 Combine like terms: 26 + -26 = 0 494 + -546x + 26x2 = 0 Factor out the Greatest Common Factor (GCF), '26'. 26(19 + -21x + x2) = 0 Ignore the factor 26.Subproblem 1
Set the factor '(19 + -21x + x2)' equal to zero and attempt to solve: Simplifying 19 + -21x + x2 = 0 Solving 19 + -21x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + -21x + -19 + x2 = 0 + -19 Reorder the terms: 19 + -19 + -21x + x2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -21x + x2 = 0 + -19 -21x + x2 = 0 + -19 Combine like terms: 0 + -19 = -19 -21x + x2 = -19 The x term is -21x. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21x + 110.25 + x2 = -19 + 110.25 Reorder the terms: 110.25 + -21x + x2 = -19 + 110.25 Combine like terms: -19 + 110.25 = 91.25 110.25 + -21x + x2 = 91.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 91.25 Calculate the square root of the right side: 9.552486587 Break this problem into two subproblems by setting (x + -10.5) equal to 9.552486587 and -9.552486587.Subproblem 1
x + -10.5 = 9.552486587 Simplifying x + -10.5 = 9.552486587 Reorder the terms: -10.5 + x = 9.552486587 Solving -10.5 + x = 9.552486587 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = 9.552486587 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 9.552486587 + 10.5 x = 9.552486587 + 10.5 Combine like terms: 9.552486587 + 10.5 = 20.052486587 x = 20.052486587 Simplifying x = 20.052486587Subproblem 2
x + -10.5 = -9.552486587 Simplifying x + -10.5 = -9.552486587 Reorder the terms: -10.5 + x = -9.552486587 Solving -10.5 + x = -9.552486587 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = -9.552486587 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -9.552486587 + 10.5 x = -9.552486587 + 10.5 Combine like terms: -9.552486587 + 10.5 = 0.947513413 x = 0.947513413 Simplifying x = 0.947513413Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.052486587, 0.947513413}Solution
x = {20.052486587, 0.947513413}
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