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Simplifying 17x2 + 14x + -8 = 0 Reorder the terms: -8 + 14x + 17x2 = 0 Solving -8 + 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'. -0.4705882353 + 0.8235294118x + x2 = 0 Move the constant term to the right: Add '0.4705882353' to each side of the equation. -0.4705882353 + 0.8235294118x + 0.4705882353 + x2 = 0 + 0.4705882353 Reorder the terms: -0.4705882353 + 0.4705882353 + 0.8235294118x + x2 = 0 + 0.4705882353 Combine like terms: -0.4705882353 + 0.4705882353 = 0.0000000000 0.0000000000 + 0.8235294118x + x2 = 0 + 0.4705882353 0.8235294118x + x2 = 0 + 0.4705882353 Combine like terms: 0 + 0.4705882353 = 0.4705882353 0.8235294118x + x2 = 0.4705882353 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 = 0.4705882353 + 0.1695501730 Reorder the terms: 0.1695501730 + 0.8235294118x + x2 = 0.4705882353 + 0.1695501730 Combine like terms: 0.4705882353 + 0.1695501730 = 0.6401384083 0.1695501730 + 0.8235294118x + x2 = 0.6401384083 Factor a perfect square on the left side: (x + 0.4117647059)(x + 0.4117647059) = 0.6401384083 Calculate the square root of the right side: 0.800086501 Break this problem into two subproblems by setting (x + 0.4117647059) equal to 0.800086501 and -0.800086501.Subproblem 1
x + 0.4117647059 = 0.800086501 Simplifying x + 0.4117647059 = 0.800086501 Reorder the terms: 0.4117647059 + x = 0.800086501 Solving 0.4117647059 + x = 0.800086501 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 = 0.800086501 + -0.4117647059 Combine like terms: 0.4117647059 + -0.4117647059 = 0.0000000000 0.0000000000 + x = 0.800086501 + -0.4117647059 x = 0.800086501 + -0.4117647059 Combine like terms: 0.800086501 + -0.4117647059 = 0.3883217951 x = 0.3883217951 Simplifying x = 0.3883217951Subproblem 2
x + 0.4117647059 = -0.800086501 Simplifying x + 0.4117647059 = -0.800086501 Reorder the terms: 0.4117647059 + x = -0.800086501 Solving 0.4117647059 + x = -0.800086501 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 = -0.800086501 + -0.4117647059 Combine like terms: 0.4117647059 + -0.4117647059 = 0.0000000000 0.0000000000 + x = -0.800086501 + -0.4117647059 x = -0.800086501 + -0.4117647059 Combine like terms: -0.800086501 + -0.4117647059 = -1.2118512069 x = -1.2118512069 Simplifying x = -1.2118512069Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3883217951, -1.2118512069}
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