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Simplifying 9x2 + -17x + 7 = 0 Reorder the terms: 7 + -17x + 9x2 = 0 Solving 7 + -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'. 0.7777777778 + -1.888888889x + x2 = 0 Move the constant term to the right: Add '-0.7777777778' to each side of the equation. 0.7777777778 + -1.888888889x + -0.7777777778 + x2 = 0 + -0.7777777778 Reorder the terms: 0.7777777778 + -0.7777777778 + -1.888888889x + x2 = 0 + -0.7777777778 Combine like terms: 0.7777777778 + -0.7777777778 = 0.0000000000 0.0000000000 + -1.888888889x + x2 = 0 + -0.7777777778 -1.888888889x + x2 = 0 + -0.7777777778 Combine like terms: 0 + -0.7777777778 = -0.7777777778 -1.888888889x + x2 = -0.7777777778 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 = -0.7777777778 + 0.8919753087 Reorder the terms: 0.8919753087 + -1.888888889x + x2 = -0.7777777778 + 0.8919753087 Combine like terms: -0.7777777778 + 0.8919753087 = 0.1141975309 0.8919753087 + -1.888888889x + x2 = 0.1141975309 Factor a perfect square on the left side: (x + -0.9444444445)(x + -0.9444444445) = 0.1141975309 Calculate the square root of the right side: 0.337931252 Break this problem into two subproblems by setting (x + -0.9444444445) equal to 0.337931252 and -0.337931252.Subproblem 1
x + -0.9444444445 = 0.337931252 Simplifying x + -0.9444444445 = 0.337931252 Reorder the terms: -0.9444444445 + x = 0.337931252 Solving -0.9444444445 + x = 0.337931252 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 = 0.337931252 + 0.9444444445 Combine like terms: -0.9444444445 + 0.9444444445 = 0.0000000000 0.0000000000 + x = 0.337931252 + 0.9444444445 x = 0.337931252 + 0.9444444445 Combine like terms: 0.337931252 + 0.9444444445 = 1.2823756965 x = 1.2823756965 Simplifying x = 1.2823756965Subproblem 2
x + -0.9444444445 = -0.337931252 Simplifying x + -0.9444444445 = -0.337931252 Reorder the terms: -0.9444444445 + x = -0.337931252 Solving -0.9444444445 + x = -0.337931252 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 = -0.337931252 + 0.9444444445 Combine like terms: -0.9444444445 + 0.9444444445 = 0.0000000000 0.0000000000 + x = -0.337931252 + 0.9444444445 x = -0.337931252 + 0.9444444445 Combine like terms: -0.337931252 + 0.9444444445 = 0.6065131925 x = 0.6065131925 Simplifying x = 0.6065131925Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2823756965, 0.6065131925}
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