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Simplifying 71.1 = x + x2 Solving 71.1 = x + x2 Solving for variable 'x'. Reorder the terms: 71.1 + -1x + -1x2 = x + -1x + x2 + -1x2 Combine like terms: x + -1x = 0 71.1 + -1x + -1x2 = 0 + x2 + -1x2 71.1 + -1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 71.1 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -71.1 + x + x2 = 0 Move the constant term to the right: Add '71.1' to each side of the equation. -71.1 + x + 71.1 + x2 = 0 + 71.1 Reorder the terms: -71.1 + 71.1 + x + x2 = 0 + 71.1 Combine like terms: -71.1 + 71.1 = 0.0 0.0 + x + x2 = 0 + 71.1 x + x2 = 0 + 71.1 Combine like terms: 0 + 71.1 = 71.1 x + x2 = 71.1 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. + 0.25 + x2 = 71.1 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 71.1 + 0.25 Combine like terms: 71.1 + 0.25 = 71.35 1.25 + x2 = 71.35 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 71.35 Calculate the square root of the right side: 8.44689292 Break this problem into two subproblems by setting (x + 0.5) equal to 8.44689292 and -8.44689292.Subproblem 1
x + 0.5 = 8.44689292 Simplifying x + 0.5 = 8.44689292 Reorder the terms: 0.5 + x = 8.44689292 Solving 0.5 + x = 8.44689292 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 = 8.44689292 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 8.44689292 + -0.5 x = 8.44689292 + -0.5 Combine like terms: 8.44689292 + -0.5 = 7.94689292 x = 7.94689292 Simplifying x = 7.94689292Subproblem 2
x + 0.5 = -8.44689292 Simplifying x + 0.5 = -8.44689292 Reorder the terms: 0.5 + x = -8.44689292 Solving 0.5 + x = -8.44689292 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 = -8.44689292 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -8.44689292 + -0.5 x = -8.44689292 + -0.5 Combine like terms: -8.44689292 + -0.5 = -8.94689292 x = -8.94689292 Simplifying x = -8.94689292Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.94689292, -8.94689292}
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