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Simplifying 9x2 + -170x + -143 = 0 Reorder the terms: -143 + -170x + 9x2 = 0 Solving -143 + -170x + 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'. -15.88888889 + -18.88888889x + x2 = 0 Move the constant term to the right: Add '15.88888889' to each side of the equation. -15.88888889 + -18.88888889x + 15.88888889 + x2 = 0 + 15.88888889 Reorder the terms: -15.88888889 + 15.88888889 + -18.88888889x + x2 = 0 + 15.88888889 Combine like terms: -15.88888889 + 15.88888889 = 0.00000000 0.00000000 + -18.88888889x + x2 = 0 + 15.88888889 -18.88888889x + x2 = 0 + 15.88888889 Combine like terms: 0 + 15.88888889 = 15.88888889 -18.88888889x + x2 = 15.88888889 The x term is -18.88888889x. Take half its coefficient (-9.444444445). Square it (89.19753087) and add it to both sides. Add '89.19753087' to each side of the equation. -18.88888889x + 89.19753087 + x2 = 15.88888889 + 89.19753087 Reorder the terms: 89.19753087 + -18.88888889x + x2 = 15.88888889 + 89.19753087 Combine like terms: 15.88888889 + 89.19753087 = 105.08641976 89.19753087 + -18.88888889x + x2 = 105.08641976 Factor a perfect square on the left side: (x + -9.444444445)(x + -9.444444445) = 105.08641976 Calculate the square root of the right side: 10.251166751 Break this problem into two subproblems by setting (x + -9.444444445) equal to 10.251166751 and -10.251166751.Subproblem 1
x + -9.444444445 = 10.251166751 Simplifying x + -9.444444445 = 10.251166751 Reorder the terms: -9.444444445 + x = 10.251166751 Solving -9.444444445 + x = 10.251166751 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.444444445' to each side of the equation. -9.444444445 + 9.444444445 + x = 10.251166751 + 9.444444445 Combine like terms: -9.444444445 + 9.444444445 = 0.000000000 0.000000000 + x = 10.251166751 + 9.444444445 x = 10.251166751 + 9.444444445 Combine like terms: 10.251166751 + 9.444444445 = 19.695611196 x = 19.695611196 Simplifying x = 19.695611196Subproblem 2
x + -9.444444445 = -10.251166751 Simplifying x + -9.444444445 = -10.251166751 Reorder the terms: -9.444444445 + x = -10.251166751 Solving -9.444444445 + x = -10.251166751 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.444444445' to each side of the equation. -9.444444445 + 9.444444445 + x = -10.251166751 + 9.444444445 Combine like terms: -9.444444445 + 9.444444445 = 0.000000000 0.000000000 + x = -10.251166751 + 9.444444445 x = -10.251166751 + 9.444444445 Combine like terms: -10.251166751 + 9.444444445 = -0.806722306 x = -0.806722306 Simplifying x = -0.806722306Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.695611196, -0.806722306}
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