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Simplifying 4x2 + 4x + 1 = 41 Reorder the terms: 1 + 4x + 4x2 = 41 Solving 1 + 4x + 4x2 = 41 Solving for variable 'x'. Reorder the terms: 1 + -41 + 4x + 4x2 = 41 + -41 Combine like terms: 1 + -41 = -40 -40 + 4x + 4x2 = 41 + -41 Combine like terms: 41 + -41 = 0 -40 + 4x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-10 + x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-10 + x + x2)' equal to zero and attempt to solve: Simplifying -10 + x + x2 = 0 Solving -10 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + x + x2 = 0 + 10 x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 x + x2 = 10 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 = 10 + 0.25 Reorder the terms: 0.25 + x + x2 = 10 + 0.25 Combine like terms: 10 + 0.25 = 10.25 0.25 + x + x2 = 10.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (x + 0.5) equal to 3.201562119 and -3.201562119.Subproblem 1
x + 0.5 = 3.201562119 Simplifying x + 0.5 = 3.201562119 Reorder the terms: 0.5 + x = 3.201562119 Solving 0.5 + x = 3.201562119 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 = 3.201562119 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.201562119 + -0.5 x = 3.201562119 + -0.5 Combine like terms: 3.201562119 + -0.5 = 2.701562119 x = 2.701562119 Simplifying x = 2.701562119Subproblem 2
x + 0.5 = -3.201562119 Simplifying x + 0.5 = -3.201562119 Reorder the terms: 0.5 + x = -3.201562119 Solving 0.5 + x = -3.201562119 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 = -3.201562119 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.201562119 + -0.5 x = -3.201562119 + -0.5 Combine like terms: -3.201562119 + -0.5 = -3.701562119 x = -3.701562119 Simplifying x = -3.701562119Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.701562119, -3.701562119}Solution
x = {2.701562119, -3.701562119}
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