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Simplifying 23 + x * 23 = 4x2 Reorder the terms for easier multiplication: 23 + 23x = 4x2 Solving 23 + 23x = 4x2 Solving for variable 'x'. Combine like terms: 4x2 + -4x2 = 0 23 + 23x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -5.75 + -5.75x + x2 = 0 Move the constant term to the right: Add '5.75' to each side of the equation. -5.75 + -5.75x + 5.75 + x2 = 0 + 5.75 Reorder the terms: -5.75 + 5.75 + -5.75x + x2 = 0 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + -5.75x + x2 = 0 + 5.75 -5.75x + x2 = 0 + 5.75 Combine like terms: 0 + 5.75 = 5.75 -5.75x + x2 = 5.75 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 = 5.75 + 8.265625 Reorder the terms: 8.265625 + -5.75x + x2 = 5.75 + 8.265625 Combine like terms: 5.75 + 8.265625 = 14.015625 8.265625 + -5.75x + x2 = 14.015625 Factor a perfect square on the left side: (x + -2.875)(x + -2.875) = 14.015625 Calculate the square root of the right side: 3.743744783 Break this problem into two subproblems by setting (x + -2.875) equal to 3.743744783 and -3.743744783.Subproblem 1
x + -2.875 = 3.743744783 Simplifying x + -2.875 = 3.743744783 Reorder the terms: -2.875 + x = 3.743744783 Solving -2.875 + x = 3.743744783 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 = 3.743744783 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = 3.743744783 + 2.875 x = 3.743744783 + 2.875 Combine like terms: 3.743744783 + 2.875 = 6.618744783 x = 6.618744783 Simplifying x = 6.618744783Subproblem 2
x + -2.875 = -3.743744783 Simplifying x + -2.875 = -3.743744783 Reorder the terms: -2.875 + x = -3.743744783 Solving -2.875 + x = -3.743744783 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 = -3.743744783 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = -3.743744783 + 2.875 x = -3.743744783 + 2.875 Combine like terms: -3.743744783 + 2.875 = -0.868744783 x = -0.868744783 Simplifying x = -0.868744783Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.618744783, -0.868744783}
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