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Simplifying 0 = 7.6x2 + -7.6x + 1 Reorder the terms: 0 = 1 + -7.6x + 7.6x2 Solving 0 = 1 + -7.6x + 7.6x2 Solving for variable 'x'. Combine like terms: 0 + -1 = -1 -1 + 7.6x + -7.6x2 = 1 + -7.6x + 7.6x2 + -1 + 7.6x + -7.6x2 Reorder the terms: -1 + 7.6x + -7.6x2 = 1 + -1 + -7.6x + 7.6x + 7.6x2 + -7.6x2 Combine like terms: 1 + -1 = 0 -1 + 7.6x + -7.6x2 = 0 + -7.6x + 7.6x + 7.6x2 + -7.6x2 -1 + 7.6x + -7.6x2 = -7.6x + 7.6x + 7.6x2 + -7.6x2 Combine like terms: -7.6x + 7.6x = 0.0 -1 + 7.6x + -7.6x2 = 0.0 + 7.6x2 + -7.6x2 -1 + 7.6x + -7.6x2 = 7.6x2 + -7.6x2 Combine like terms: 7.6x2 + -7.6x2 = 0.0 -1 + 7.6x + -7.6x2 = 0.0 Begin completing the square. Divide all terms by -7.6 the coefficient of the squared term: Divide each side by '-7.6'. 0.1315789474 + -1x + x2 = 0 Move the constant term to the right: Add '-0.1315789474' to each side of the equation. 0.1315789474 + -1x + -0.1315789474 + x2 = 0 + -0.1315789474 Reorder the terms: 0.1315789474 + -0.1315789474 + -1x + x2 = 0 + -0.1315789474 Combine like terms: 0.1315789474 + -0.1315789474 = 0.0000000000 0.0000000000 + -1x + x2 = 0 + -0.1315789474 -1x + x2 = 0 + -0.1315789474 Combine like terms: 0 + -0.1315789474 = -0.1315789474 -1x + x2 = -0.1315789474 The x term is -1x. 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. -1x + 0.25 + x2 = -0.1315789474 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.1315789474 + 0.25 Combine like terms: -0.1315789474 + 0.25 = 0.1184210526 0.25 + -1x + x2 = 0.1184210526 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.1184210526 Calculate the square root of the right side: 0.344123601 Break this problem into two subproblems by setting (x + -0.5) equal to 0.344123601 and -0.344123601.Subproblem 1
x + -0.5 = 0.344123601 Simplifying x + -0.5 = 0.344123601 Reorder the terms: -0.5 + x = 0.344123601 Solving -0.5 + x = 0.344123601 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 = 0.344123601 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.344123601 + 0.5 x = 0.344123601 + 0.5 Combine like terms: 0.344123601 + 0.5 = 0.844123601 x = 0.844123601 Simplifying x = 0.844123601Subproblem 2
x + -0.5 = -0.344123601 Simplifying x + -0.5 = -0.344123601 Reorder the terms: -0.5 + x = -0.344123601 Solving -0.5 + x = -0.344123601 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 = -0.344123601 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.344123601 + 0.5 x = -0.344123601 + 0.5 Combine like terms: -0.344123601 + 0.5 = 0.155876399 x = 0.155876399 Simplifying x = 0.155876399Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.844123601, 0.155876399}
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