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Simplifying 4x2 + -68x + 268 = 0 Reorder the terms: 268 + -68x + 4x2 = 0 Solving 268 + -68x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(67 + -17x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(67 + -17x + x2)' equal to zero and attempt to solve: Simplifying 67 + -17x + x2 = 0 Solving 67 + -17x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-67' to each side of the equation. 67 + -17x + -67 + x2 = 0 + -67 Reorder the terms: 67 + -67 + -17x + x2 = 0 + -67 Combine like terms: 67 + -67 = 0 0 + -17x + x2 = 0 + -67 -17x + x2 = 0 + -67 Combine like terms: 0 + -67 = -67 -17x + x2 = -67 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = -67 + 72.25 Reorder the terms: 72.25 + -17x + x2 = -67 + 72.25 Combine like terms: -67 + 72.25 = 5.25 72.25 + -17x + x2 = 5.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (x + -8.5) equal to 2.291287847 and -2.291287847.Subproblem 1
x + -8.5 = 2.291287847 Simplifying x + -8.5 = 2.291287847 Reorder the terms: -8.5 + x = 2.291287847 Solving -8.5 + x = 2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 2.291287847 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 2.291287847 + 8.5 x = 2.291287847 + 8.5 Combine like terms: 2.291287847 + 8.5 = 10.791287847 x = 10.791287847 Simplifying x = 10.791287847Subproblem 2
x + -8.5 = -2.291287847 Simplifying x + -8.5 = -2.291287847 Reorder the terms: -8.5 + x = -2.291287847 Solving -8.5 + x = -2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -2.291287847 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -2.291287847 + 8.5 x = -2.291287847 + 8.5 Combine like terms: -2.291287847 + 8.5 = 6.208712153 x = 6.208712153 Simplifying x = 6.208712153Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.791287847, 6.208712153}Solution
x = {10.791287847, 6.208712153}
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