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Simplifying 9x2 + -17x + -85 = 0 Reorder the terms: -85 + -17x + 9x2 = 0 Solving -85 + -17x + 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'. -9.444444444 + -1.888888889x + x2 = 0 Move the constant term to the right: Add '9.444444444' to each side of the equation. -9.444444444 + -1.888888889x + 9.444444444 + x2 = 0 + 9.444444444 Reorder the terms: -9.444444444 + 9.444444444 + -1.888888889x + x2 = 0 + 9.444444444 Combine like terms: -9.444444444 + 9.444444444 = 0.000000000 0.000000000 + -1.888888889x + x2 = 0 + 9.444444444 -1.888888889x + x2 = 0 + 9.444444444 Combine like terms: 0 + 9.444444444 = 9.444444444 -1.888888889x + x2 = 9.444444444 The x term is -1.888888889x. Take half its coefficient (-0.9444444445). Square it (0.8919753087) and add it to both sides. Add '0.8919753087' to each side of the equation. -1.888888889x + 0.8919753087 + x2 = 9.444444444 + 0.8919753087 Reorder the terms: 0.8919753087 + -1.888888889x + x2 = 9.444444444 + 0.8919753087 Combine like terms: 9.444444444 + 0.8919753087 = 10.3364197527 0.8919753087 + -1.888888889x + x2 = 10.3364197527 Factor a perfect square on the left side: (x + -0.9444444445)(x + -0.9444444445) = 10.3364197527 Calculate the square root of the right side: 3.215030288 Break this problem into two subproblems by setting (x + -0.9444444445) equal to 3.215030288 and -3.215030288.Subproblem 1
x + -0.9444444445 = 3.215030288 Simplifying x + -0.9444444445 = 3.215030288 Reorder the terms: -0.9444444445 + x = 3.215030288 Solving -0.9444444445 + x = 3.215030288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9444444445' to each side of the equation. -0.9444444445 + 0.9444444445 + x = 3.215030288 + 0.9444444445 Combine like terms: -0.9444444445 + 0.9444444445 = 0.0000000000 0.0000000000 + x = 3.215030288 + 0.9444444445 x = 3.215030288 + 0.9444444445 Combine like terms: 3.215030288 + 0.9444444445 = 4.1594747325 x = 4.1594747325 Simplifying x = 4.1594747325Subproblem 2
x + -0.9444444445 = -3.215030288 Simplifying x + -0.9444444445 = -3.215030288 Reorder the terms: -0.9444444445 + x = -3.215030288 Solving -0.9444444445 + x = -3.215030288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9444444445' to each side of the equation. -0.9444444445 + 0.9444444445 + x = -3.215030288 + 0.9444444445 Combine like terms: -0.9444444445 + 0.9444444445 = 0.0000000000 0.0000000000 + x = -3.215030288 + 0.9444444445 x = -3.215030288 + 0.9444444445 Combine like terms: -3.215030288 + 0.9444444445 = -2.2705858435 x = -2.2705858435 Simplifying x = -2.2705858435Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.1594747325, -2.2705858435}
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