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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 = 1.6697530865 0.8919753087 + 1.888888889x + x2 = 1.6697530865 Factor a perfect square on the left side: (x + 0.9444444445)(x + 0.9444444445) = 1.6697530865 Calculate the square root of the right side: 1.292189261 Break this problem into two subproblems by setting (x + 0.9444444445) equal to 1.292189261 and -1.292189261.Subproblem 1
x + 0.9444444445 = 1.292189261 Simplifying x + 0.9444444445 = 1.292189261 Reorder the terms: 0.9444444445 + x = 1.292189261 Solving 0.9444444445 + x = 1.292189261 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 = 1.292189261 + -0.9444444445 Combine like terms: 0.9444444445 + -0.9444444445 = 0.0000000000 0.0000000000 + x = 1.292189261 + -0.9444444445 x = 1.292189261 + -0.9444444445 Combine like terms: 1.292189261 + -0.9444444445 = 0.3477448165 x = 0.3477448165 Simplifying x = 0.3477448165Subproblem 2
x + 0.9444444445 = -1.292189261 Simplifying x + 0.9444444445 = -1.292189261 Reorder the terms: 0.9444444445 + x = -1.292189261 Solving 0.9444444445 + x = -1.292189261 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 = -1.292189261 + -0.9444444445 Combine like terms: 0.9444444445 + -0.9444444445 = 0.0000000000 0.0000000000 + x = -1.292189261 + -0.9444444445 x = -1.292189261 + -0.9444444445 Combine like terms: -1.292189261 + -0.9444444445 = -2.2366337055 x = -2.2366337055 Simplifying x = -2.2366337055Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3477448165, -2.2366337055}
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