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Simplifying 2x2 + 2x + -76 = 0 Reorder the terms: -76 + 2x + 2x2 = 0 Solving -76 + 2x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-38 + x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-38 + x + x2)' equal to zero and attempt to solve: Simplifying -38 + x + x2 = 0 Solving -38 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '38' to each side of the equation. -38 + x + 38 + x2 = 0 + 38 Reorder the terms: -38 + 38 + x + x2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + x + x2 = 0 + 38 x + x2 = 0 + 38 Combine like terms: 0 + 38 = 38 x + x2 = 38 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 = 38 + 0.25 Reorder the terms: 0.25 + x + x2 = 38 + 0.25 Combine like terms: 38 + 0.25 = 38.25 0.25 + x + x2 = 38.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (x + 0.5) equal to 6.184658438 and -6.184658438.Subproblem 1
x + 0.5 = 6.184658438 Simplifying x + 0.5 = 6.184658438 Reorder the terms: 0.5 + x = 6.184658438 Solving 0.5 + x = 6.184658438 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 = 6.184658438 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 6.184658438 + -0.5 x = 6.184658438 + -0.5 Combine like terms: 6.184658438 + -0.5 = 5.684658438 x = 5.684658438 Simplifying x = 5.684658438Subproblem 2
x + 0.5 = -6.184658438 Simplifying x + 0.5 = -6.184658438 Reorder the terms: 0.5 + x = -6.184658438 Solving 0.5 + x = -6.184658438 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 = -6.184658438 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -6.184658438 + -0.5 x = -6.184658438 + -0.5 Combine like terms: -6.184658438 + -0.5 = -6.684658438 x = -6.684658438 Simplifying x = -6.684658438Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.684658438, -6.684658438}Solution
x = {5.684658438, -6.684658438}
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