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Simplifying x2 + 0.76x = 1.44 Reorder the terms: 0.76x + x2 = 1.44 Solving 0.76x + x2 = 1.44 Solving for variable 'x'. Reorder the terms: -1.44 + 0.76x + x2 = 1.44 + -1.44 Combine like terms: 1.44 + -1.44 = 0.00 -1.44 + 0.76x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '1.44' to each side of the equation. -1.44 + 0.76x + 1.44 + x2 = 0.00 + 1.44 Reorder the terms: -1.44 + 1.44 + 0.76x + x2 = 0.00 + 1.44 Combine like terms: -1.44 + 1.44 = 0.00 0.00 + 0.76x + x2 = 0.00 + 1.44 0.76x + x2 = 0.00 + 1.44 Combine like terms: 0.00 + 1.44 = 1.44 0.76x + x2 = 1.44 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 = 1.44 + 0.1444 Reorder the terms: 0.1444 + 0.76x + x2 = 1.44 + 0.1444 Combine like terms: 1.44 + 0.1444 = 1.5844 0.1444 + 0.76x + x2 = 1.5844 Factor a perfect square on the left side: (x + 0.38)(x + 0.38) = 1.5844 Calculate the square root of the right side: 1.258729518 Break this problem into two subproblems by setting (x + 0.38) equal to 1.258729518 and -1.258729518.Subproblem 1
x + 0.38 = 1.258729518 Simplifying x + 0.38 = 1.258729518 Reorder the terms: 0.38 + x = 1.258729518 Solving 0.38 + x = 1.258729518 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 = 1.258729518 + -0.38 Combine like terms: 0.38 + -0.38 = 0.00 0.00 + x = 1.258729518 + -0.38 x = 1.258729518 + -0.38 Combine like terms: 1.258729518 + -0.38 = 0.878729518 x = 0.878729518 Simplifying x = 0.878729518Subproblem 2
x + 0.38 = -1.258729518 Simplifying x + 0.38 = -1.258729518 Reorder the terms: 0.38 + x = -1.258729518 Solving 0.38 + x = -1.258729518 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 = -1.258729518 + -0.38 Combine like terms: 0.38 + -0.38 = 0.00 0.00 + x = -1.258729518 + -0.38 x = -1.258729518 + -0.38 Combine like terms: -1.258729518 + -0.38 = -1.638729518 x = -1.638729518 Simplifying x = -1.638729518Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.878729518, -1.638729518}
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