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Simplifying 4.25(x)(x) + -3.17x + -6.95 = 0 Multiply x * x 4.25x2 + -3.17x + -6.95 = 0 Reorder the terms: -6.95 + -3.17x + 4.25x2 = 0 Solving -6.95 + -3.17x + 4.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.25 the coefficient of the squared term: Divide each side by '4.25'. -1.635294118 + -0.7458823529x + x2 = 0 Move the constant term to the right: Add '1.635294118' to each side of the equation. -1.635294118 + -0.7458823529x + 1.635294118 + x2 = 0 + 1.635294118 Reorder the terms: -1.635294118 + 1.635294118 + -0.7458823529x + x2 = 0 + 1.635294118 Combine like terms: -1.635294118 + 1.635294118 = 0.000000000 0.000000000 + -0.7458823529x + x2 = 0 + 1.635294118 -0.7458823529x + x2 = 0 + 1.635294118 Combine like terms: 0 + 1.635294118 = 1.635294118 -0.7458823529x + x2 = 1.635294118 The x term is -0.7458823529x. Take half its coefficient (-0.3729411765). Square it (0.1390851211) and add it to both sides. Add '0.1390851211' to each side of the equation. -0.7458823529x + 0.1390851211 + x2 = 1.635294118 + 0.1390851211 Reorder the terms: 0.1390851211 + -0.7458823529x + x2 = 1.635294118 + 0.1390851211 Combine like terms: 1.635294118 + 0.1390851211 = 1.7743792391 0.1390851211 + -0.7458823529x + x2 = 1.7743792391 Factor a perfect square on the left side: (x + -0.3729411765)(x + -0.3729411765) = 1.7743792391 Calculate the square root of the right side: 1.332058272 Break this problem into two subproblems by setting (x + -0.3729411765) equal to 1.332058272 and -1.332058272.Subproblem 1
x + -0.3729411765 = 1.332058272 Simplifying x + -0.3729411765 = 1.332058272 Reorder the terms: -0.3729411765 + x = 1.332058272 Solving -0.3729411765 + x = 1.332058272 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3729411765' to each side of the equation. -0.3729411765 + 0.3729411765 + x = 1.332058272 + 0.3729411765 Combine like terms: -0.3729411765 + 0.3729411765 = 0.0000000000 0.0000000000 + x = 1.332058272 + 0.3729411765 x = 1.332058272 + 0.3729411765 Combine like terms: 1.332058272 + 0.3729411765 = 1.7049994485 x = 1.7049994485 Simplifying x = 1.7049994485Subproblem 2
x + -0.3729411765 = -1.332058272 Simplifying x + -0.3729411765 = -1.332058272 Reorder the terms: -0.3729411765 + x = -1.332058272 Solving -0.3729411765 + x = -1.332058272 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3729411765' to each side of the equation. -0.3729411765 + 0.3729411765 + x = -1.332058272 + 0.3729411765 Combine like terms: -0.3729411765 + 0.3729411765 = 0.0000000000 0.0000000000 + x = -1.332058272 + 0.3729411765 x = -1.332058272 + 0.3729411765 Combine like terms: -1.332058272 + 0.3729411765 = -0.9591170955 x = -0.9591170955 Simplifying x = -0.9591170955Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7049994485, -0.9591170955}
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