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Simplifying 2x(x + -10) + -2(x + 5) = 0 Reorder the terms: 2x(-10 + x) + -2(x + 5) = 0 (-10 * 2x + x * 2x) + -2(x + 5) = 0 (-20x + 2x2) + -2(x + 5) = 0 Reorder the terms: -20x + 2x2 + -2(5 + x) = 0 -20x + 2x2 + (5 * -2 + x * -2) = 0 -20x + 2x2 + (-10 + -2x) = 0 Reorder the terms: -10 + -20x + -2x + 2x2 = 0 Combine like terms: -20x + -2x = -22x -10 + -22x + 2x2 = 0 Solving -10 + -22x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -11x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -11x + x2)' equal to zero and attempt to solve: Simplifying -5 + -11x + x2 = 0 Solving -5 + -11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -11x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -11x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -11x + x2 = 0 + 5 -11x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -11x + x2 = 5 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = 5 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 5 + 30.25 Combine like terms: 5 + 30.25 = 35.25 30.25 + -11x + x2 = 35.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 35.25 Calculate the square root of the right side: 5.937171044 Break this problem into two subproblems by setting (x + -5.5) equal to 5.937171044 and -5.937171044.Subproblem 1
x + -5.5 = 5.937171044 Simplifying x + -5.5 = 5.937171044 Reorder the terms: -5.5 + x = 5.937171044 Solving -5.5 + x = 5.937171044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 5.937171044 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 5.937171044 + 5.5 x = 5.937171044 + 5.5 Combine like terms: 5.937171044 + 5.5 = 11.437171044 x = 11.437171044 Simplifying x = 11.437171044Subproblem 2
x + -5.5 = -5.937171044 Simplifying x + -5.5 = -5.937171044 Reorder the terms: -5.5 + x = -5.937171044 Solving -5.5 + x = -5.937171044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -5.937171044 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -5.937171044 + 5.5 x = -5.937171044 + 5.5 Combine like terms: -5.937171044 + 5.5 = -0.437171044 x = -0.437171044 Simplifying x = -0.437171044Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.437171044, -0.437171044}Solution
x = {11.437171044, -0.437171044}
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