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Simplifying 48x2 + -28x = 3 Reorder the terms: -28x + 48x2 = 3 Solving -28x + 48x2 = 3 Solving for variable 'x'. Reorder the terms: -3 + -28x + 48x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -28x + 48x2 = 0 Begin completing the square. Divide all terms by 48 the coefficient of the squared term: Divide each side by '48'. -0.0625 + -0.5833333333x + x2 = 0 Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + -0.5833333333x + 0.0625 + x2 = 0 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + -0.5833333333x + x2 = 0 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + -0.5833333333x + x2 = 0 + 0.0625 -0.5833333333x + x2 = 0 + 0.0625 Combine like terms: 0 + 0.0625 = 0.0625 -0.5833333333x + x2 = 0.0625 The x term is -0.5833333333x. Take half its coefficient (-0.2916666667). Square it (0.08506944446) and add it to both sides. Add '0.08506944446' to each side of the equation. -0.5833333333x + 0.08506944446 + x2 = 0.0625 + 0.08506944446 Reorder the terms: 0.08506944446 + -0.5833333333x + x2 = 0.0625 + 0.08506944446 Combine like terms: 0.0625 + 0.08506944446 = 0.14756944446 0.08506944446 + -0.5833333333x + x2 = 0.14756944446 Factor a perfect square on the left side: (x + -0.2916666667)(x + -0.2916666667) = 0.14756944446 Calculate the square root of the right side: 0.384147686 Break this problem into two subproblems by setting (x + -0.2916666667) equal to 0.384147686 and -0.384147686.Subproblem 1
x + -0.2916666667 = 0.384147686 Simplifying x + -0.2916666667 = 0.384147686 Reorder the terms: -0.2916666667 + x = 0.384147686 Solving -0.2916666667 + x = 0.384147686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2916666667' to each side of the equation. -0.2916666667 + 0.2916666667 + x = 0.384147686 + 0.2916666667 Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000 0.0000000000 + x = 0.384147686 + 0.2916666667 x = 0.384147686 + 0.2916666667 Combine like terms: 0.384147686 + 0.2916666667 = 0.6758143527 x = 0.6758143527 Simplifying x = 0.6758143527Subproblem 2
x + -0.2916666667 = -0.384147686 Simplifying x + -0.2916666667 = -0.384147686 Reorder the terms: -0.2916666667 + x = -0.384147686 Solving -0.2916666667 + x = -0.384147686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2916666667' to each side of the equation. -0.2916666667 + 0.2916666667 + x = -0.384147686 + 0.2916666667 Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000 0.0000000000 + x = -0.384147686 + 0.2916666667 x = -0.384147686 + 0.2916666667 Combine like terms: -0.384147686 + 0.2916666667 = -0.0924810193 x = -0.0924810193 Simplifying x = -0.0924810193Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6758143527, -0.0924810193}
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