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Simplifying 4x2 + -42x + 18 = 0 Reorder the terms: 18 + -42x + 4x2 = 0 Solving 18 + -42x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(9 + -21x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + -21x + 2x2)' equal to zero and attempt to solve: Simplifying 9 + -21x + 2x2 = 0 Solving 9 + -21x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4.5 + -10.5x + x2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + -10.5x + -4.5 + x2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + -10.5x + x2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + -10.5x + x2 = 0 + -4.5 -10.5x + x2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 -10.5x + x2 = -4.5 The x term is -10.5x. Take half its coefficient (-5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. -10.5x + 27.5625 + x2 = -4.5 + 27.5625 Reorder the terms: 27.5625 + -10.5x + x2 = -4.5 + 27.5625 Combine like terms: -4.5 + 27.5625 = 23.0625 27.5625 + -10.5x + x2 = 23.0625 Factor a perfect square on the left side: (x + -5.25)(x + -5.25) = 23.0625 Calculate the square root of the right side: 4.802343178 Break this problem into two subproblems by setting (x + -5.25) equal to 4.802343178 and -4.802343178.Subproblem 1
x + -5.25 = 4.802343178 Simplifying x + -5.25 = 4.802343178 Reorder the terms: -5.25 + x = 4.802343178 Solving -5.25 + x = 4.802343178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = 4.802343178 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = 4.802343178 + 5.25 x = 4.802343178 + 5.25 Combine like terms: 4.802343178 + 5.25 = 10.052343178 x = 10.052343178 Simplifying x = 10.052343178Subproblem 2
x + -5.25 = -4.802343178 Simplifying x + -5.25 = -4.802343178 Reorder the terms: -5.25 + x = -4.802343178 Solving -5.25 + x = -4.802343178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = -4.802343178 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = -4.802343178 + 5.25 x = -4.802343178 + 5.25 Combine like terms: -4.802343178 + 5.25 = 0.447656822 x = 0.447656822 Simplifying x = 0.447656822Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.052343178, 0.447656822}Solution
x = {10.052343178, 0.447656822}
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