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Simplifying 9x2 + -71x + 3 = 0 Reorder the terms: 3 + -71x + 9x2 = 0 Solving 3 + -71x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.3333333333 + -7.888888889x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -7.888888889x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -7.888888889x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -7.888888889x + x2 = 0 + -0.3333333333 -7.888888889x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -7.888888889x + x2 = -0.3333333333 The x term is -7.888888889x. Take half its coefficient (-3.944444445). Square it (15.55864198) and add it to both sides. Add '15.55864198' to each side of the equation. -7.888888889x + 15.55864198 + x2 = -0.3333333333 + 15.55864198 Reorder the terms: 15.55864198 + -7.888888889x + x2 = -0.3333333333 + 15.55864198 Combine like terms: -0.3333333333 + 15.55864198 = 15.2253086467 15.55864198 + -7.888888889x + x2 = 15.2253086467 Factor a perfect square on the left side: (x + -3.944444445)(x + -3.944444445) = 15.2253086467 Calculate the square root of the right side: 3.901962153 Break this problem into two subproblems by setting (x + -3.944444445) equal to 3.901962153 and -3.901962153.Subproblem 1
x + -3.944444445 = 3.901962153 Simplifying x + -3.944444445 = 3.901962153 Reorder the terms: -3.944444445 + x = 3.901962153 Solving -3.944444445 + x = 3.901962153 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.944444445' to each side of the equation. -3.944444445 + 3.944444445 + x = 3.901962153 + 3.944444445 Combine like terms: -3.944444445 + 3.944444445 = 0.000000000 0.000000000 + x = 3.901962153 + 3.944444445 x = 3.901962153 + 3.944444445 Combine like terms: 3.901962153 + 3.944444445 = 7.846406598 x = 7.846406598 Simplifying x = 7.846406598Subproblem 2
x + -3.944444445 = -3.901962153 Simplifying x + -3.944444445 = -3.901962153 Reorder the terms: -3.944444445 + x = -3.901962153 Solving -3.944444445 + x = -3.901962153 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.944444445' to each side of the equation. -3.944444445 + 3.944444445 + x = -3.901962153 + 3.944444445 Combine like terms: -3.944444445 + 3.944444445 = 0.000000000 0.000000000 + x = -3.901962153 + 3.944444445 x = -3.901962153 + 3.944444445 Combine like terms: -3.901962153 + 3.944444445 = 0.042482292 x = 0.042482292 Simplifying x = 0.042482292Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.846406598, 0.042482292}
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