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Simplifying 2x2 + 8x + -76 = 0 Reorder the terms: -76 + 8x + 2x2 = 0 Solving -76 + 8x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-38 + 4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-38 + 4x + x2)' equal to zero and attempt to solve: Simplifying -38 + 4x + x2 = 0 Solving -38 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '38' to each side of the equation. -38 + 4x + 38 + x2 = 0 + 38 Reorder the terms: -38 + 38 + 4x + x2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + 4x + x2 = 0 + 38 4x + x2 = 0 + 38 Combine like terms: 0 + 38 = 38 4x + x2 = 38 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 38 + 4 Reorder the terms: 4 + 4x + x2 = 38 + 4 Combine like terms: 38 + 4 = 42 4 + 4x + x2 = 42 Factor a perfect square on the left side: (x + 2)(x + 2) = 42 Calculate the square root of the right side: 6.480740698 Break this problem into two subproblems by setting (x + 2) equal to 6.480740698 and -6.480740698.Subproblem 1
x + 2 = 6.480740698 Simplifying x + 2 = 6.480740698 Reorder the terms: 2 + x = 6.480740698 Solving 2 + x = 6.480740698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 6.480740698 + -2 Combine like terms: 2 + -2 = 0 0 + x = 6.480740698 + -2 x = 6.480740698 + -2 Combine like terms: 6.480740698 + -2 = 4.480740698 x = 4.480740698 Simplifying x = 4.480740698Subproblem 2
x + 2 = -6.480740698 Simplifying x + 2 = -6.480740698 Reorder the terms: 2 + x = -6.480740698 Solving 2 + x = -6.480740698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -6.480740698 + -2 Combine like terms: 2 + -2 = 0 0 + x = -6.480740698 + -2 x = -6.480740698 + -2 Combine like terms: -6.480740698 + -2 = -8.480740698 x = -8.480740698 Simplifying x = -8.480740698Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.480740698, -8.480740698}Solution
x = {4.480740698, -8.480740698}
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