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Simplifying 20x2 + 23x = 12 Reorder the terms: 23x + 20x2 = 12 Solving 23x + 20x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + 23x + 20x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 23x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.6 + 1.15x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + 1.15x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + 1.15x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + 1.15x + x2 = 0 + 0.6 1.15x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 1.15x + x2 = 0.6 The x term is 1.15x. Take half its coefficient (0.575). Square it (0.330625) and add it to both sides. Add '0.330625' to each side of the equation. 1.15x + 0.330625 + x2 = 0.6 + 0.330625 Reorder the terms: 0.330625 + 1.15x + x2 = 0.6 + 0.330625 Combine like terms: 0.6 + 0.330625 = 0.930625 0.330625 + 1.15x + x2 = 0.930625 Factor a perfect square on the left side: (x + 0.575)(x + 0.575) = 0.930625 Calculate the square root of the right side: 0.964689069 Break this problem into two subproblems by setting (x + 0.575) equal to 0.964689069 and -0.964689069.Subproblem 1
x + 0.575 = 0.964689069 Simplifying x + 0.575 = 0.964689069 Reorder the terms: 0.575 + x = 0.964689069 Solving 0.575 + x = 0.964689069 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.575' to each side of the equation. 0.575 + -0.575 + x = 0.964689069 + -0.575 Combine like terms: 0.575 + -0.575 = 0.000 0.000 + x = 0.964689069 + -0.575 x = 0.964689069 + -0.575 Combine like terms: 0.964689069 + -0.575 = 0.389689069 x = 0.389689069 Simplifying x = 0.389689069Subproblem 2
x + 0.575 = -0.964689069 Simplifying x + 0.575 = -0.964689069 Reorder the terms: 0.575 + x = -0.964689069 Solving 0.575 + x = -0.964689069 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.575' to each side of the equation. 0.575 + -0.575 + x = -0.964689069 + -0.575 Combine like terms: 0.575 + -0.575 = 0.000 0.000 + x = -0.964689069 + -0.575 x = -0.964689069 + -0.575 Combine like terms: -0.964689069 + -0.575 = -1.539689069 x = -1.539689069 Simplifying x = -1.539689069Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.389689069, -1.539689069}
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