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Simplifying 2x2 + 2x + 3 = 11 Reorder the terms: 3 + 2x + 2x2 = 11 Solving 3 + 2x + 2x2 = 11 Solving for variable 'x'. Reorder the terms: 3 + -11 + 2x + 2x2 = 11 + -11 Combine like terms: 3 + -11 = -8 -8 + 2x + 2x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -8 + 2x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + x + x2)' equal to zero and attempt to solve: Simplifying -4 + x + x2 = 0 Solving -4 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x + x2 = 0 + 4 x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 x + x2 = 4 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 = 4 + 0.25 Reorder the terms: 0.25 + x + x2 = 4 + 0.25 Combine like terms: 4 + 0.25 = 4.25 0.25 + x + x2 = 4.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x + 0.5) equal to 2.061552813 and -2.061552813.Subproblem 1
x + 0.5 = 2.061552813 Simplifying x + 0.5 = 2.061552813 Reorder the terms: 0.5 + x = 2.061552813 Solving 0.5 + x = 2.061552813 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 = 2.061552813 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.061552813 + -0.5 x = 2.061552813 + -0.5 Combine like terms: 2.061552813 + -0.5 = 1.561552813 x = 1.561552813 Simplifying x = 1.561552813Subproblem 2
x + 0.5 = -2.061552813 Simplifying x + 0.5 = -2.061552813 Reorder the terms: 0.5 + x = -2.061552813 Solving 0.5 + x = -2.061552813 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 = -2.061552813 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.061552813 + -0.5 x = -2.061552813 + -0.5 Combine like terms: -2.061552813 + -0.5 = -2.561552813 x = -2.561552813 Simplifying x = -2.561552813Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.561552813, -2.561552813}Solution
x = {1.561552813, -2.561552813}
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