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Simplifying x2 + 0.76x = 0.988 Reorder the terms: 0.76x + x2 = 0.988 Solving 0.76x + x2 = 0.988 Solving for variable 'x'. Reorder the terms: -0.988 + 0.76x + x2 = 0.988 + -0.988 Combine like terms: 0.988 + -0.988 = 0.000 -0.988 + 0.76x + x2 = 0.000 Begin completing the square. Move the constant term to the right: Add '0.988' to each side of the equation. -0.988 + 0.76x + 0.988 + x2 = 0.000 + 0.988 Reorder the terms: -0.988 + 0.988 + 0.76x + x2 = 0.000 + 0.988 Combine like terms: -0.988 + 0.988 = 0.000 0.000 + 0.76x + x2 = 0.000 + 0.988 0.76x + x2 = 0.000 + 0.988 Combine like terms: 0.000 + 0.988 = 0.988 0.76x + x2 = 0.988 The x term is 0.76x. Take half its coefficient (0.38). Square it (0.1444) and add it to both sides. Add '0.1444' to each side of the equation. 0.76x + 0.1444 + x2 = 0.988 + 0.1444 Reorder the terms: 0.1444 + 0.76x + x2 = 0.988 + 0.1444 Combine like terms: 0.988 + 0.1444 = 1.1324 0.1444 + 0.76x + x2 = 1.1324 Factor a perfect square on the left side: (x + 0.38)(x + 0.38) = 1.1324 Calculate the square root of the right side: 1.064142848 Break this problem into two subproblems by setting (x + 0.38) equal to 1.064142848 and -1.064142848.Subproblem 1
x + 0.38 = 1.064142848 Simplifying x + 0.38 = 1.064142848 Reorder the terms: 0.38 + x = 1.064142848 Solving 0.38 + x = 1.064142848 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.38' to each side of the equation. 0.38 + -0.38 + x = 1.064142848 + -0.38 Combine like terms: 0.38 + -0.38 = 0.00 0.00 + x = 1.064142848 + -0.38 x = 1.064142848 + -0.38 Combine like terms: 1.064142848 + -0.38 = 0.684142848 x = 0.684142848 Simplifying x = 0.684142848Subproblem 2
x + 0.38 = -1.064142848 Simplifying x + 0.38 = -1.064142848 Reorder the terms: 0.38 + x = -1.064142848 Solving 0.38 + x = -1.064142848 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.38' to each side of the equation. 0.38 + -0.38 + x = -1.064142848 + -0.38 Combine like terms: 0.38 + -0.38 = 0.00 0.00 + x = -1.064142848 + -0.38 x = -1.064142848 + -0.38 Combine like terms: -1.064142848 + -0.38 = -1.444142848 x = -1.444142848 Simplifying x = -1.444142848Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.684142848, -1.444142848}
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