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Simplifying 2x(x + -10) + 4 = 6x + 2 Reorder the terms: 2x(-10 + x) + 4 = 6x + 2 (-10 * 2x + x * 2x) + 4 = 6x + 2 (-20x + 2x2) + 4 = 6x + 2 Reorder the terms: 4 + -20x + 2x2 = 6x + 2 Reorder the terms: 4 + -20x + 2x2 = 2 + 6x Solving 4 + -20x + 2x2 = 2 + 6x Solving for variable 'x'. Reorder the terms: 4 + -2 + -20x + -6x + 2x2 = 2 + 6x + -2 + -6x Combine like terms: 4 + -2 = 2 2 + -20x + -6x + 2x2 = 2 + 6x + -2 + -6x Combine like terms: -20x + -6x = -26x 2 + -26x + 2x2 = 2 + 6x + -2 + -6x Reorder the terms: 2 + -26x + 2x2 = 2 + -2 + 6x + -6x Combine like terms: 2 + -2 = 0 2 + -26x + 2x2 = 0 + 6x + -6x 2 + -26x + 2x2 = 6x + -6x Combine like terms: 6x + -6x = 0 2 + -26x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -13x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -13x + x2)' equal to zero and attempt to solve: Simplifying 1 + -13x + x2 = 0 Solving 1 + -13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -13x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -13x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -13x + x2 = 0 + -1 -13x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -13x + x2 = -1 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = -1 + 42.25 Reorder the terms: 42.25 + -13x + x2 = -1 + 42.25 Combine like terms: -1 + 42.25 = 41.25 42.25 + -13x + x2 = 41.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 41.25 Calculate the square root of the right side: 6.422616289 Break this problem into two subproblems by setting (x + -6.5) equal to 6.422616289 and -6.422616289.Subproblem 1
x + -6.5 = 6.422616289 Simplifying x + -6.5 = 6.422616289 Reorder the terms: -6.5 + x = 6.422616289 Solving -6.5 + x = 6.422616289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 6.422616289 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 6.422616289 + 6.5 x = 6.422616289 + 6.5 Combine like terms: 6.422616289 + 6.5 = 12.922616289 x = 12.922616289 Simplifying x = 12.922616289Subproblem 2
x + -6.5 = -6.422616289 Simplifying x + -6.5 = -6.422616289 Reorder the terms: -6.5 + x = -6.422616289 Solving -6.5 + x = -6.422616289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -6.422616289 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -6.422616289 + 6.5 x = -6.422616289 + 6.5 Combine like terms: -6.422616289 + 6.5 = 0.077383711 x = 0.077383711 Simplifying x = 0.077383711Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.922616289, 0.077383711}Solution
x = {12.922616289, 0.077383711}
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