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Simplifying x(2x + 2) = 42 Reorder the terms: x(2 + 2x) = 42 (2 * x + 2x * x) = 42 (2x + 2x2) = 42 Solving 2x + 2x2 = 42 Solving for variable 'x'. Reorder the terms: -42 + 2x + 2x2 = 42 + -42 Combine like terms: 42 + -42 = 0 -42 + 2x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-21 + x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-21 + x + x2)' equal to zero and attempt to solve: Simplifying -21 + x + x2 = 0 Solving -21 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + x + x2 = 0 + 21 x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 x + x2 = 21 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 21 + 0.25 Reorder the terms: 0.25 + x + x2 = 21 + 0.25 Combine like terms: 21 + 0.25 = 21.25 0.25 + x + x2 = 21.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (x + 0.5) equal to 4.609772229 and -4.609772229.Subproblem 1
x + 0.5 = 4.609772229 Simplifying x + 0.5 = 4.609772229 Reorder the terms: 0.5 + x = 4.609772229 Solving 0.5 + x = 4.609772229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 4.609772229 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.609772229 + -0.5 x = 4.609772229 + -0.5 Combine like terms: 4.609772229 + -0.5 = 4.109772229 x = 4.109772229 Simplifying x = 4.109772229Subproblem 2
x + 0.5 = -4.609772229 Simplifying x + 0.5 = -4.609772229 Reorder the terms: 0.5 + x = -4.609772229 Solving 0.5 + x = -4.609772229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -4.609772229 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.609772229 + -0.5 x = -4.609772229 + -0.5 Combine like terms: -4.609772229 + -0.5 = -5.109772229 x = -5.109772229 Simplifying x = -5.109772229Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.109772229, -5.109772229}Solution
x = {4.109772229, -5.109772229}
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