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Simplifying 3x2 + -96x + 102 = 0 Reorder the terms: 102 + -96x + 3x2 = 0 Solving 102 + -96x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(34 + -32x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(34 + -32x + x2)' equal to zero and attempt to solve: Simplifying 34 + -32x + x2 = 0 Solving 34 + -32x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-34' to each side of the equation. 34 + -32x + -34 + x2 = 0 + -34 Reorder the terms: 34 + -34 + -32x + x2 = 0 + -34 Combine like terms: 34 + -34 = 0 0 + -32x + x2 = 0 + -34 -32x + x2 = 0 + -34 Combine like terms: 0 + -34 = -34 -32x + x2 = -34 The x term is -32x. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32x + 256 + x2 = -34 + 256 Reorder the terms: 256 + -32x + x2 = -34 + 256 Combine like terms: -34 + 256 = 222 256 + -32x + x2 = 222 Factor a perfect square on the left side: (x + -16)(x + -16) = 222 Calculate the square root of the right side: 14.899664426 Break this problem into two subproblems by setting (x + -16) equal to 14.899664426 and -14.899664426.Subproblem 1
x + -16 = 14.899664426 Simplifying x + -16 = 14.899664426 Reorder the terms: -16 + x = 14.899664426 Solving -16 + x = 14.899664426 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 14.899664426 + 16 Combine like terms: -16 + 16 = 0 0 + x = 14.899664426 + 16 x = 14.899664426 + 16 Combine like terms: 14.899664426 + 16 = 30.899664426 x = 30.899664426 Simplifying x = 30.899664426Subproblem 2
x + -16 = -14.899664426 Simplifying x + -16 = -14.899664426 Reorder the terms: -16 + x = -14.899664426 Solving -16 + x = -14.899664426 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = -14.899664426 + 16 Combine like terms: -16 + 16 = 0 0 + x = -14.899664426 + 16 x = -14.899664426 + 16 Combine like terms: -14.899664426 + 16 = 1.100335574 x = 1.100335574 Simplifying x = 1.100335574Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.899664426, 1.100335574}Solution
x = {30.899664426, 1.100335574}
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