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Simplifying 2x2 + 32x + 42 = 0 Reorder the terms: 42 + 32x + 2x2 = 0 Solving 42 + 32x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(21 + 16x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(21 + 16x + x2)' equal to zero and attempt to solve: Simplifying 21 + 16x + x2 = 0 Solving 21 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + 16x + -21 + x2 = 0 + -21 Reorder the terms: 21 + -21 + 16x + x2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 16x + x2 = 0 + -21 16x + x2 = 0 + -21 Combine like terms: 0 + -21 = -21 16x + x2 = -21 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = -21 + 64 Reorder the terms: 64 + 16x + x2 = -21 + 64 Combine like terms: -21 + 64 = 43 64 + 16x + x2 = 43 Factor a perfect square on the left side: (x + 8)(x + 8) = 43 Calculate the square root of the right side: 6.557438524 Break this problem into two subproblems by setting (x + 8) equal to 6.557438524 and -6.557438524.Subproblem 1
x + 8 = 6.557438524 Simplifying x + 8 = 6.557438524 Reorder the terms: 8 + x = 6.557438524 Solving 8 + x = 6.557438524 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 6.557438524 + -8 Combine like terms: 8 + -8 = 0 0 + x = 6.557438524 + -8 x = 6.557438524 + -8 Combine like terms: 6.557438524 + -8 = -1.442561476 x = -1.442561476 Simplifying x = -1.442561476Subproblem 2
x + 8 = -6.557438524 Simplifying x + 8 = -6.557438524 Reorder the terms: 8 + x = -6.557438524 Solving 8 + x = -6.557438524 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -6.557438524 + -8 Combine like terms: 8 + -8 = 0 0 + x = -6.557438524 + -8 x = -6.557438524 + -8 Combine like terms: -6.557438524 + -8 = -14.557438524 x = -14.557438524 Simplifying x = -14.557438524Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.442561476, -14.557438524}Solution
x = {-1.442561476, -14.557438524}
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