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Simplifying -16x2 + 54x + 2 = 62x Reorder the terms: 2 + 54x + -16x2 = 62x Solving 2 + 54x + -16x2 = 62x Solving for variable 'x'. Reorder the terms: 2 + 54x + -62x + -16x2 = 62x + -62x Combine like terms: 54x + -62x = -8x 2 + -8x + -16x2 = 62x + -62x Combine like terms: 62x + -62x = 0 2 + -8x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -4x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -4x + -8x2)' equal to zero and attempt to solve: Simplifying 1 + -4x + -8x2 = 0 Solving 1 + -4x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.125 + 0.5x + x2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + 0.5x + 0.125 + x2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + 0.5x + x2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + 0.5x + x2 = 0 + 0.125 0.5x + x2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 0.5x + x2 = 0.125 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 0.125 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 0.125 + 0.0625 Combine like terms: 0.125 + 0.0625 = 0.1875 0.0625 + 0.5x + x2 = 0.1875 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 0.1875 Calculate the square root of the right side: 0.433012702 Break this problem into two subproblems by setting (x + 0.25) equal to 0.433012702 and -0.433012702.Subproblem 1
x + 0.25 = 0.433012702 Simplifying x + 0.25 = 0.433012702 Reorder the terms: 0.25 + x = 0.433012702 Solving 0.25 + x = 0.433012702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 0.433012702 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 0.433012702 + -0.25 x = 0.433012702 + -0.25 Combine like terms: 0.433012702 + -0.25 = 0.183012702 x = 0.183012702 Simplifying x = 0.183012702Subproblem 2
x + 0.25 = -0.433012702 Simplifying x + 0.25 = -0.433012702 Reorder the terms: 0.25 + x = -0.433012702 Solving 0.25 + x = -0.433012702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -0.433012702 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -0.433012702 + -0.25 x = -0.433012702 + -0.25 Combine like terms: -0.433012702 + -0.25 = -0.683012702 x = -0.683012702 Simplifying x = -0.683012702Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.183012702, -0.683012702}Solution
x = {0.183012702, -0.683012702}
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