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Simplifying 4x2 = 146 + -32x Solving 4x2 = 146 + -32x Solving for variable 'x'. Reorder the terms: -146 + 32x + 4x2 = 146 + -32x + -146 + 32x Reorder the terms: -146 + 32x + 4x2 = 146 + -146 + -32x + 32x Combine like terms: 146 + -146 = 0 -146 + 32x + 4x2 = 0 + -32x + 32x -146 + 32x + 4x2 = -32x + 32x Combine like terms: -32x + 32x = 0 -146 + 32x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-73 + 16x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-73 + 16x + 2x2)' equal to zero and attempt to solve: Simplifying -73 + 16x + 2x2 = 0 Solving -73 + 16x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -36.5 + 8x + x2 = 0 Move the constant term to the right: Add '36.5' to each side of the equation. -36.5 + 8x + 36.5 + x2 = 0 + 36.5 Reorder the terms: -36.5 + 36.5 + 8x + x2 = 0 + 36.5 Combine like terms: -36.5 + 36.5 = 0.0 0.0 + 8x + x2 = 0 + 36.5 8x + x2 = 0 + 36.5 Combine like terms: 0 + 36.5 = 36.5 8x + x2 = 36.5 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 36.5 + 16 Reorder the terms: 16 + 8x + x2 = 36.5 + 16 Combine like terms: 36.5 + 16 = 52.5 16 + 8x + x2 = 52.5 Factor a perfect square on the left side: (x + 4)(x + 4) = 52.5 Calculate the square root of the right side: 7.245688373 Break this problem into two subproblems by setting (x + 4) equal to 7.245688373 and -7.245688373.Subproblem 1
x + 4 = 7.245688373 Simplifying x + 4 = 7.245688373 Reorder the terms: 4 + x = 7.245688373 Solving 4 + x = 7.245688373 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 7.245688373 + -4 Combine like terms: 4 + -4 = 0 0 + x = 7.245688373 + -4 x = 7.245688373 + -4 Combine like terms: 7.245688373 + -4 = 3.245688373 x = 3.245688373 Simplifying x = 3.245688373Subproblem 2
x + 4 = -7.245688373 Simplifying x + 4 = -7.245688373 Reorder the terms: 4 + x = -7.245688373 Solving 4 + x = -7.245688373 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -7.245688373 + -4 Combine like terms: 4 + -4 = 0 0 + x = -7.245688373 + -4 x = -7.245688373 + -4 Combine like terms: -7.245688373 + -4 = -11.245688373 x = -11.245688373 Simplifying x = -11.245688373Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.245688373, -11.245688373}Solution
x = {3.245688373, -11.245688373}
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