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Simplifying 9x2 + -17x + -56 = 0 Reorder the terms: -56 + -17x + 9x2 = 0 Solving -56 + -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'. -6.222222222 + -1.888888889x + x2 = 0 Move the constant term to the right: Add '6.222222222' to each side of the equation. -6.222222222 + -1.888888889x + 6.222222222 + x2 = 0 + 6.222222222 Reorder the terms: -6.222222222 + 6.222222222 + -1.888888889x + x2 = 0 + 6.222222222 Combine like terms: -6.222222222 + 6.222222222 = 0.000000000 0.000000000 + -1.888888889x + x2 = 0 + 6.222222222 -1.888888889x + x2 = 0 + 6.222222222 Combine like terms: 0 + 6.222222222 = 6.222222222 -1.888888889x + x2 = 6.222222222 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 = 6.222222222 + 0.8919753087 Reorder the terms: 0.8919753087 + -1.888888889x + x2 = 6.222222222 + 0.8919753087 Combine like terms: 6.222222222 + 0.8919753087 = 7.1141975307 0.8919753087 + -1.888888889x + x2 = 7.1141975307 Factor a perfect square on the left side: (x + -0.9444444445)(x + -0.9444444445) = 7.1141975307 Calculate the square root of the right side: 2.667245308 Break this problem into two subproblems by setting (x + -0.9444444445) equal to 2.667245308 and -2.667245308.Subproblem 1
x + -0.9444444445 = 2.667245308 Simplifying x + -0.9444444445 = 2.667245308 Reorder the terms: -0.9444444445 + x = 2.667245308 Solving -0.9444444445 + x = 2.667245308 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 = 2.667245308 + 0.9444444445 Combine like terms: -0.9444444445 + 0.9444444445 = 0.0000000000 0.0000000000 + x = 2.667245308 + 0.9444444445 x = 2.667245308 + 0.9444444445 Combine like terms: 2.667245308 + 0.9444444445 = 3.6116897525 x = 3.6116897525 Simplifying x = 3.6116897525Subproblem 2
x + -0.9444444445 = -2.667245308 Simplifying x + -0.9444444445 = -2.667245308 Reorder the terms: -0.9444444445 + x = -2.667245308 Solving -0.9444444445 + x = -2.667245308 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 = -2.667245308 + 0.9444444445 Combine like terms: -0.9444444445 + 0.9444444445 = 0.0000000000 0.0000000000 + x = -2.667245308 + 0.9444444445 x = -2.667245308 + 0.9444444445 Combine like terms: -2.667245308 + 0.9444444445 = -1.7228008635 x = -1.7228008635 Simplifying x = -1.7228008635Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.6116897525, -1.7228008635}
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