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Simplifying 9x2 + 17x + -55 = 9 Reorder the terms: -55 + 17x + 9x2 = 9 Solving -55 + 17x + 9x2 = 9 Solving for variable 'x'. Reorder the terms: -55 + -9 + 17x + 9x2 = 9 + -9 Combine like terms: -55 + -9 = -64 -64 + 17x + 9x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -64 + 17x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -7.111111111 + 1.888888889x + x2 = 0 Move the constant term to the right: Add '7.111111111' to each side of the equation. -7.111111111 + 1.888888889x + 7.111111111 + x2 = 0 + 7.111111111 Reorder the terms: -7.111111111 + 7.111111111 + 1.888888889x + x2 = 0 + 7.111111111 Combine like terms: -7.111111111 + 7.111111111 = 0.000000000 0.000000000 + 1.888888889x + x2 = 0 + 7.111111111 1.888888889x + x2 = 0 + 7.111111111 Combine like terms: 0 + 7.111111111 = 7.111111111 1.888888889x + x2 = 7.111111111 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 = 7.111111111 + 0.8919753087 Reorder the terms: 0.8919753087 + 1.888888889x + x2 = 7.111111111 + 0.8919753087 Combine like terms: 7.111111111 + 0.8919753087 = 8.0030864197 0.8919753087 + 1.888888889x + x2 = 8.0030864197 Factor a perfect square on the left side: (x + 0.9444444445)(x + 0.9444444445) = 8.0030864197 Calculate the square root of the right side: 2.828972679 Break this problem into two subproblems by setting (x + 0.9444444445) equal to 2.828972679 and -2.828972679.Subproblem 1
x + 0.9444444445 = 2.828972679 Simplifying x + 0.9444444445 = 2.828972679 Reorder the terms: 0.9444444445 + x = 2.828972679 Solving 0.9444444445 + x = 2.828972679 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 = 2.828972679 + -0.9444444445 Combine like terms: 0.9444444445 + -0.9444444445 = 0.0000000000 0.0000000000 + x = 2.828972679 + -0.9444444445 x = 2.828972679 + -0.9444444445 Combine like terms: 2.828972679 + -0.9444444445 = 1.8845282345 x = 1.8845282345 Simplifying x = 1.8845282345Subproblem 2
x + 0.9444444445 = -2.828972679 Simplifying x + 0.9444444445 = -2.828972679 Reorder the terms: 0.9444444445 + x = -2.828972679 Solving 0.9444444445 + x = -2.828972679 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 = -2.828972679 + -0.9444444445 Combine like terms: 0.9444444445 + -0.9444444445 = 0.0000000000 0.0000000000 + x = -2.828972679 + -0.9444444445 x = -2.828972679 + -0.9444444445 Combine like terms: -2.828972679 + -0.9444444445 = -3.7734171235 x = -3.7734171235 Simplifying x = -3.7734171235Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8845282345, -3.7734171235}
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