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Simplifying 18 + 17x2 + -36x = 0 Reorder the terms: 18 + -36x + 17x2 = 0 Solving 18 + -36x + 17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. 1.058823529 + -2.117647059x + x2 = 0 Move the constant term to the right: Add '-1.058823529' to each side of the equation. 1.058823529 + -2.117647059x + -1.058823529 + x2 = 0 + -1.058823529 Reorder the terms: 1.058823529 + -1.058823529 + -2.117647059x + x2 = 0 + -1.058823529 Combine like terms: 1.058823529 + -1.058823529 = 0.000000000 0.000000000 + -2.117647059x + x2 = 0 + -1.058823529 -2.117647059x + x2 = 0 + -1.058823529 Combine like terms: 0 + -1.058823529 = -1.058823529 -2.117647059x + x2 = -1.058823529 The x term is -2.117647059x. Take half its coefficient (-1.05882353). Square it (1.121107268) and add it to both sides. Add '1.121107268' to each side of the equation. -2.117647059x + 1.121107268 + x2 = -1.058823529 + 1.121107268 Reorder the terms: 1.121107268 + -2.117647059x + x2 = -1.058823529 + 1.121107268 Combine like terms: -1.058823529 + 1.121107268 = 0.062283739 1.121107268 + -2.117647059x + x2 = 0.062283739 Factor a perfect square on the left side: (x + -1.05882353)(x + -1.05882353) = 0.062283739 Calculate the square root of the right side: 0.249567103 Break this problem into two subproblems by setting (x + -1.05882353) equal to 0.249567103 and -0.249567103.Subproblem 1
x + -1.05882353 = 0.249567103 Simplifying x + -1.05882353 = 0.249567103 Reorder the terms: -1.05882353 + x = 0.249567103 Solving -1.05882353 + x = 0.249567103 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.05882353' to each side of the equation. -1.05882353 + 1.05882353 + x = 0.249567103 + 1.05882353 Combine like terms: -1.05882353 + 1.05882353 = 0.00000000 0.00000000 + x = 0.249567103 + 1.05882353 x = 0.249567103 + 1.05882353 Combine like terms: 0.249567103 + 1.05882353 = 1.308390633 x = 1.308390633 Simplifying x = 1.308390633Subproblem 2
x + -1.05882353 = -0.249567103 Simplifying x + -1.05882353 = -0.249567103 Reorder the terms: -1.05882353 + x = -0.249567103 Solving -1.05882353 + x = -0.249567103 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.05882353' to each side of the equation. -1.05882353 + 1.05882353 + x = -0.249567103 + 1.05882353 Combine like terms: -1.05882353 + 1.05882353 = 0.00000000 0.00000000 + x = -0.249567103 + 1.05882353 x = -0.249567103 + 1.05882353 Combine like terms: -0.249567103 + 1.05882353 = 0.809256427 x = 0.809256427 Simplifying x = 0.809256427Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.308390633, 0.809256427}
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