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Simplifying X + 7X2 + -63 = 8 Reorder the terms: -63 + X + 7X2 = 8 Solving -63 + X + 7X2 = 8 Solving for variable 'X'. Reorder the terms: -63 + -8 + X + 7X2 = 8 + -8 Combine like terms: -63 + -8 = -71 -71 + X + 7X2 = 8 + -8 Combine like terms: 8 + -8 = 0 -71 + X + 7X2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -10.14285714 + 0.1428571429X + X2 = 0 Move the constant term to the right: Add '10.14285714' to each side of the equation. -10.14285714 + 0.1428571429X + 10.14285714 + X2 = 0 + 10.14285714 Reorder the terms: -10.14285714 + 10.14285714 + 0.1428571429X + X2 = 0 + 10.14285714 Combine like terms: -10.14285714 + 10.14285714 = 0.00000000 0.00000000 + 0.1428571429X + X2 = 0 + 10.14285714 0.1428571429X + X2 = 0 + 10.14285714 Combine like terms: 0 + 10.14285714 = 10.14285714 0.1428571429X + X2 = 10.14285714 The X term is X. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1428571429X + 0.25 + X2 = 10.14285714 + 0.25 Reorder the terms: 0.25 + 0.1428571429X + X2 = 10.14285714 + 0.25 Combine like terms: 10.14285714 + 0.25 = 10.39285714 0.25 + 0.1428571429X + X2 = 10.39285714 Factor a perfect square on the left side: (X + 0.5)(X + 0.5) = 10.39285714 Calculate the square root of the right side: 3.223795456 Break this problem into two subproblems by setting (X + 0.5) equal to 3.223795456 and -3.223795456.Subproblem 1
X + 0.5 = 3.223795456 Simplifying X + 0.5 = 3.223795456 Reorder the terms: 0.5 + X = 3.223795456 Solving 0.5 + X = 3.223795456 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X = 3.223795456 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = 3.223795456 + -0.5 X = 3.223795456 + -0.5 Combine like terms: 3.223795456 + -0.5 = 2.723795456 X = 2.723795456 Simplifying X = 2.723795456Subproblem 2
X + 0.5 = -3.223795456 Simplifying X + 0.5 = -3.223795456 Reorder the terms: 0.5 + X = -3.223795456 Solving 0.5 + X = -3.223795456 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X = -3.223795456 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = -3.223795456 + -0.5 X = -3.223795456 + -0.5 Combine like terms: -3.223795456 + -0.5 = -3.723795456 X = -3.723795456 Simplifying X = -3.723795456Solution
The solution to the problem is based on the solutions from the subproblems. X = {2.723795456, -3.723795456}
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