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Simplifying 4x2 = 23x + 5 Reorder the terms: 4x2 = 5 + 23x Solving 4x2 = 5 + 23x Solving for variable 'x'. Reorder the terms: -5 + -23x + 4x2 = 5 + 23x + -5 + -23x Reorder the terms: -5 + -23x + 4x2 = 5 + -5 + 23x + -23x Combine like terms: 5 + -5 = 0 -5 + -23x + 4x2 = 0 + 23x + -23x -5 + -23x + 4x2 = 23x + -23x Combine like terms: 23x + -23x = 0 -5 + -23x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + -5.75x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -5.75x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -5.75x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -5.75x + x2 = 0 + 1.25 -5.75x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -5.75x + x2 = 1.25 The x term is -5.75x. Take half its coefficient (-2.875). Square it (8.265625) and add it to both sides. Add '8.265625' to each side of the equation. -5.75x + 8.265625 + x2 = 1.25 + 8.265625 Reorder the terms: 8.265625 + -5.75x + x2 = 1.25 + 8.265625 Combine like terms: 1.25 + 8.265625 = 9.515625 8.265625 + -5.75x + x2 = 9.515625 Factor a perfect square on the left side: (x + -2.875)(x + -2.875) = 9.515625 Calculate the square root of the right side: 3.08474067 Break this problem into two subproblems by setting (x + -2.875) equal to 3.08474067 and -3.08474067.Subproblem 1
x + -2.875 = 3.08474067 Simplifying x + -2.875 = 3.08474067 Reorder the terms: -2.875 + x = 3.08474067 Solving -2.875 + x = 3.08474067 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + x = 3.08474067 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = 3.08474067 + 2.875 x = 3.08474067 + 2.875 Combine like terms: 3.08474067 + 2.875 = 5.95974067 x = 5.95974067 Simplifying x = 5.95974067Subproblem 2
x + -2.875 = -3.08474067 Simplifying x + -2.875 = -3.08474067 Reorder the terms: -2.875 + x = -3.08474067 Solving -2.875 + x = -3.08474067 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + x = -3.08474067 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = -3.08474067 + 2.875 x = -3.08474067 + 2.875 Combine like terms: -3.08474067 + 2.875 = -0.20974067 x = -0.20974067 Simplifying x = -0.20974067Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.95974067, -0.20974067}
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