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Simplifying 17x2 + 14x + -56 = 0 Reorder the terms: -56 + 14x + 17x2 = 0 Solving -56 + 14x + 17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -3.294117647 + 0.8235294118x + x2 = 0 Move the constant term to the right: Add '3.294117647' to each side of the equation. -3.294117647 + 0.8235294118x + 3.294117647 + x2 = 0 + 3.294117647 Reorder the terms: -3.294117647 + 3.294117647 + 0.8235294118x + x2 = 0 + 3.294117647 Combine like terms: -3.294117647 + 3.294117647 = 0.000000000 0.000000000 + 0.8235294118x + x2 = 0 + 3.294117647 0.8235294118x + x2 = 0 + 3.294117647 Combine like terms: 0 + 3.294117647 = 3.294117647 0.8235294118x + x2 = 3.294117647 The x term is 0.8235294118x. Take half its coefficient (0.4117647059). Square it (0.1695501730) and add it to both sides. Add '0.1695501730' to each side of the equation. 0.8235294118x + 0.1695501730 + x2 = 3.294117647 + 0.1695501730 Reorder the terms: 0.1695501730 + 0.8235294118x + x2 = 3.294117647 + 0.1695501730 Combine like terms: 3.294117647 + 0.1695501730 = 3.46366782 0.1695501730 + 0.8235294118x + x2 = 3.46366782 Factor a perfect square on the left side: (x + 0.4117647059)(x + 0.4117647059) = 3.46366782 Calculate the square root of the right side: 1.861093179 Break this problem into two subproblems by setting (x + 0.4117647059) equal to 1.861093179 and -1.861093179.Subproblem 1
x + 0.4117647059 = 1.861093179 Simplifying x + 0.4117647059 = 1.861093179 Reorder the terms: 0.4117647059 + x = 1.861093179 Solving 0.4117647059 + x = 1.861093179 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4117647059' to each side of the equation. 0.4117647059 + -0.4117647059 + x = 1.861093179 + -0.4117647059 Combine like terms: 0.4117647059 + -0.4117647059 = 0.0000000000 0.0000000000 + x = 1.861093179 + -0.4117647059 x = 1.861093179 + -0.4117647059 Combine like terms: 1.861093179 + -0.4117647059 = 1.4493284731 x = 1.4493284731 Simplifying x = 1.4493284731Subproblem 2
x + 0.4117647059 = -1.861093179 Simplifying x + 0.4117647059 = -1.861093179 Reorder the terms: 0.4117647059 + x = -1.861093179 Solving 0.4117647059 + x = -1.861093179 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4117647059' to each side of the equation. 0.4117647059 + -0.4117647059 + x = -1.861093179 + -0.4117647059 Combine like terms: 0.4117647059 + -0.4117647059 = 0.0000000000 0.0000000000 + x = -1.861093179 + -0.4117647059 x = -1.861093179 + -0.4117647059 Combine like terms: -1.861093179 + -0.4117647059 = -2.2728578849 x = -2.2728578849 Simplifying x = -2.2728578849Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4493284731, -2.2728578849}
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