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Simplifying x = 0.1x2 + -0.7x + 1.4 Reorder the terms: x = 1.4 + -0.7x + 0.1x2 Solving x = 1.4 + -0.7x + 0.1x2 Solving for variable 'x'. Reorder the terms: -1.4 + x + 0.7x + -0.1x2 = 1.4 + -0.7x + 0.1x2 + -1.4 + 0.7x + -0.1x2 Combine like terms: x + 0.7x = 1.7x -1.4 + 1.7x + -0.1x2 = 1.4 + -0.7x + 0.1x2 + -1.4 + 0.7x + -0.1x2 Reorder the terms: -1.4 + 1.7x + -0.1x2 = 1.4 + -1.4 + -0.7x + 0.7x + 0.1x2 + -0.1x2 Combine like terms: 1.4 + -1.4 = 0.0 -1.4 + 1.7x + -0.1x2 = 0.0 + -0.7x + 0.7x + 0.1x2 + -0.1x2 -1.4 + 1.7x + -0.1x2 = -0.7x + 0.7x + 0.1x2 + -0.1x2 Combine like terms: -0.7x + 0.7x = 0.0 -1.4 + 1.7x + -0.1x2 = 0.0 + 0.1x2 + -0.1x2 -1.4 + 1.7x + -0.1x2 = 0.1x2 + -0.1x2 Combine like terms: 0.1x2 + -0.1x2 = 0.0 -1.4 + 1.7x + -0.1x2 = 0.0 Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. 14 + -17x + x2 = 0 Move the constant term to the right: Add '-14' to each side of the equation. 14 + -17x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + -17x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -17x + x2 = 0 + -14 -17x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 -17x + x2 = -14 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = -14 + 72.25 Reorder the terms: 72.25 + -17x + x2 = -14 + 72.25 Combine like terms: -14 + 72.25 = 58.25 72.25 + -17x + x2 = 58.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 58.25 Calculate the square root of the right side: 7.632168761 Break this problem into two subproblems by setting (x + -8.5) equal to 7.632168761 and -7.632168761.Subproblem 1
x + -8.5 = 7.632168761 Simplifying x + -8.5 = 7.632168761 Reorder the terms: -8.5 + x = 7.632168761 Solving -8.5 + x = 7.632168761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 7.632168761 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 7.632168761 + 8.5 x = 7.632168761 + 8.5 Combine like terms: 7.632168761 + 8.5 = 16.132168761 x = 16.132168761 Simplifying x = 16.132168761Subproblem 2
x + -8.5 = -7.632168761 Simplifying x + -8.5 = -7.632168761 Reorder the terms: -8.5 + x = -7.632168761 Solving -8.5 + x = -7.632168761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -7.632168761 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -7.632168761 + 8.5 x = -7.632168761 + 8.5 Combine like terms: -7.632168761 + 8.5 = 0.867831239 x = 0.867831239 Simplifying x = 0.867831239Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.132168761, 0.867831239}
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