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Simplifying 4x2 + -23.76x + 5.3236 = 0 Reorder the terms: 5.3236 + -23.76x + 4x2 = 0 Solving 5.3236 + -23.76x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.3309 + -5.94x + x2 = 0 Move the constant term to the right: Add '-1.3309' to each side of the equation. 1.3309 + -5.94x + -1.3309 + x2 = 0 + -1.3309 Reorder the terms: 1.3309 + -1.3309 + -5.94x + x2 = 0 + -1.3309 Combine like terms: 1.3309 + -1.3309 = 0.0000 0.0000 + -5.94x + x2 = 0 + -1.3309 -5.94x + x2 = 0 + -1.3309 Combine like terms: 0 + -1.3309 = -1.3309 -5.94x + x2 = -1.3309 The x term is -5.94x. Take half its coefficient (-2.97). Square it (8.8209) and add it to both sides. Add '8.8209' to each side of the equation. -5.94x + 8.8209 + x2 = -1.3309 + 8.8209 Reorder the terms: 8.8209 + -5.94x + x2 = -1.3309 + 8.8209 Combine like terms: -1.3309 + 8.8209 = 7.49 8.8209 + -5.94x + x2 = 7.49 Factor a perfect square on the left side: (x + -2.97)(x + -2.97) = 7.49 Calculate the square root of the right side: 2.736786437 Break this problem into two subproblems by setting (x + -2.97) equal to 2.736786437 and -2.736786437.Subproblem 1
x + -2.97 = 2.736786437 Simplifying x + -2.97 = 2.736786437 Reorder the terms: -2.97 + x = 2.736786437 Solving -2.97 + x = 2.736786437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.97' to each side of the equation. -2.97 + 2.97 + x = 2.736786437 + 2.97 Combine like terms: -2.97 + 2.97 = 0.00 0.00 + x = 2.736786437 + 2.97 x = 2.736786437 + 2.97 Combine like terms: 2.736786437 + 2.97 = 5.706786437 x = 5.706786437 Simplifying x = 5.706786437Subproblem 2
x + -2.97 = -2.736786437 Simplifying x + -2.97 = -2.736786437 Reorder the terms: -2.97 + x = -2.736786437 Solving -2.97 + x = -2.736786437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.97' to each side of the equation. -2.97 + 2.97 + x = -2.736786437 + 2.97 Combine like terms: -2.97 + 2.97 = 0.00 0.00 + x = -2.736786437 + 2.97 x = -2.736786437 + 2.97 Combine like terms: -2.736786437 + 2.97 = 0.233213563 x = 0.233213563 Simplifying x = 0.233213563Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.706786437, 0.233213563}
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