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Simplifying x(28x + 23) = 4 Reorder the terms: x(23 + 28x) = 4 (23 * x + 28x * x) = 4 (23x + 28x2) = 4 Solving 23x + 28x2 = 4 Solving for variable 'x'. Reorder the terms: -4 + 23x + 28x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 23x + 28x2 = 0 Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -0.1428571429 + 0.8214285714x + x2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.8214285714x + 0.1428571429 + x2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + 0.8214285714x + x2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + 0.8214285714x + x2 = 0 + 0.1428571429 0.8214285714x + x2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 0.8214285714x + x2 = 0.1428571429 The x term is 0.8214285714x. Take half its coefficient (0.4107142857). Square it (0.1686862245) and add it to both sides. Add '0.1686862245' to each side of the equation. 0.8214285714x + 0.1686862245 + x2 = 0.1428571429 + 0.1686862245 Reorder the terms: 0.1686862245 + 0.8214285714x + x2 = 0.1428571429 + 0.1686862245 Combine like terms: 0.1428571429 + 0.1686862245 = 0.3115433674 0.1686862245 + 0.8214285714x + x2 = 0.3115433674 Factor a perfect square on the left side: (x + 0.4107142857)(x + 0.4107142857) = 0.3115433674 Calculate the square root of the right side: 0.5581607 Break this problem into two subproblems by setting (x + 0.4107142857) equal to 0.5581607 and -0.5581607.Subproblem 1
x + 0.4107142857 = 0.5581607 Simplifying x + 0.4107142857 = 0.5581607 Reorder the terms: 0.4107142857 + x = 0.5581607 Solving 0.4107142857 + x = 0.5581607 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4107142857' to each side of the equation. 0.4107142857 + -0.4107142857 + x = 0.5581607 + -0.4107142857 Combine like terms: 0.4107142857 + -0.4107142857 = 0.0000000000 0.0000000000 + x = 0.5581607 + -0.4107142857 x = 0.5581607 + -0.4107142857 Combine like terms: 0.5581607 + -0.4107142857 = 0.1474464143 x = 0.1474464143 Simplifying x = 0.1474464143Subproblem 2
x + 0.4107142857 = -0.5581607 Simplifying x + 0.4107142857 = -0.5581607 Reorder the terms: 0.4107142857 + x = -0.5581607 Solving 0.4107142857 + x = -0.5581607 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4107142857' to each side of the equation. 0.4107142857 + -0.4107142857 + x = -0.5581607 + -0.4107142857 Combine like terms: 0.4107142857 + -0.4107142857 = 0.0000000000 0.0000000000 + x = -0.5581607 + -0.4107142857 x = -0.5581607 + -0.4107142857 Combine like terms: -0.5581607 + -0.4107142857 = -0.9688749857 x = -0.9688749857 Simplifying x = -0.9688749857Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1474464143, -0.9688749857}
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