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Simplifying 4x2 + -42x + 27 = 0 Reorder the terms: 27 + -42x + 4x2 = 0 Solving 27 + -42x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 6.75 + -10.5x + x2 = 0 Move the constant term to the right: Add '-6.75' to each side of the equation. 6.75 + -10.5x + -6.75 + x2 = 0 + -6.75 Reorder the terms: 6.75 + -6.75 + -10.5x + x2 = 0 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + -10.5x + x2 = 0 + -6.75 -10.5x + x2 = 0 + -6.75 Combine like terms: 0 + -6.75 = -6.75 -10.5x + x2 = -6.75 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 = -6.75 + 27.5625 Reorder the terms: 27.5625 + -10.5x + x2 = -6.75 + 27.5625 Combine like terms: -6.75 + 27.5625 = 20.8125 27.5625 + -10.5x + x2 = 20.8125 Factor a perfect square on the left side: (x + -5.25)(x + -5.25) = 20.8125 Calculate the square root of the right side: 4.562071898 Break this problem into two subproblems by setting (x + -5.25) equal to 4.562071898 and -4.562071898.Subproblem 1
x + -5.25 = 4.562071898 Simplifying x + -5.25 = 4.562071898 Reorder the terms: -5.25 + x = 4.562071898 Solving -5.25 + x = 4.562071898 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 = 4.562071898 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = 4.562071898 + 5.25 x = 4.562071898 + 5.25 Combine like terms: 4.562071898 + 5.25 = 9.812071898 x = 9.812071898 Simplifying x = 9.812071898Subproblem 2
x + -5.25 = -4.562071898 Simplifying x + -5.25 = -4.562071898 Reorder the terms: -5.25 + x = -4.562071898 Solving -5.25 + x = -4.562071898 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 = -4.562071898 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = -4.562071898 + 5.25 x = -4.562071898 + 5.25 Combine like terms: -4.562071898 + 5.25 = 0.687928102 x = 0.687928102 Simplifying x = 0.687928102Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.812071898, 0.687928102}
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