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Simplifying 4.8x2 = 5.2x + 2.7 Reorder the terms: 4.8x2 = 2.7 + 5.2x Solving 4.8x2 = 2.7 + 5.2x Solving for variable 'x'. Reorder the terms: -2.7 + -5.2x + 4.8x2 = 2.7 + 5.2x + -2.7 + -5.2x Reorder the terms: -2.7 + -5.2x + 4.8x2 = 2.7 + -2.7 + 5.2x + -5.2x Combine like terms: 2.7 + -2.7 = 0.0 -2.7 + -5.2x + 4.8x2 = 0.0 + 5.2x + -5.2x -2.7 + -5.2x + 4.8x2 = 5.2x + -5.2x Combine like terms: 5.2x + -5.2x = 0.0 -2.7 + -5.2x + 4.8x2 = 0.0 Begin completing the square. Divide all terms by 4.8 the coefficient of the squared term: Divide each side by '4.8'. -0.5625 + -1.083333333x + x2 = 0 Move the constant term to the right: Add '0.5625' to each side of the equation. -0.5625 + -1.083333333x + 0.5625 + x2 = 0 + 0.5625 Reorder the terms: -0.5625 + 0.5625 + -1.083333333x + x2 = 0 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + -1.083333333x + x2 = 0 + 0.5625 -1.083333333x + x2 = 0 + 0.5625 Combine like terms: 0 + 0.5625 = 0.5625 -1.083333333x + x2 = 0.5625 The x term is -1.083333333x. Take half its coefficient (-0.5416666665). Square it (0.2934027776) and add it to both sides. Add '0.2934027776' to each side of the equation. -1.083333333x + 0.2934027776 + x2 = 0.5625 + 0.2934027776 Reorder the terms: 0.2934027776 + -1.083333333x + x2 = 0.5625 + 0.2934027776 Combine like terms: 0.5625 + 0.2934027776 = 0.8559027776 0.2934027776 + -1.083333333x + x2 = 0.8559027776 Factor a perfect square on the left side: (x + -0.5416666665)(x + -0.5416666665) = 0.8559027776 Calculate the square root of the right side: 0.925150138 Break this problem into two subproblems by setting (x + -0.5416666665) equal to 0.925150138 and -0.925150138.Subproblem 1
x + -0.5416666665 = 0.925150138 Simplifying x + -0.5416666665 = 0.925150138 Reorder the terms: -0.5416666665 + x = 0.925150138 Solving -0.5416666665 + x = 0.925150138 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5416666665' to each side of the equation. -0.5416666665 + 0.5416666665 + x = 0.925150138 + 0.5416666665 Combine like terms: -0.5416666665 + 0.5416666665 = 0.0000000000 0.0000000000 + x = 0.925150138 + 0.5416666665 x = 0.925150138 + 0.5416666665 Combine like terms: 0.925150138 + 0.5416666665 = 1.4668168045 x = 1.4668168045 Simplifying x = 1.4668168045Subproblem 2
x + -0.5416666665 = -0.925150138 Simplifying x + -0.5416666665 = -0.925150138 Reorder the terms: -0.5416666665 + x = -0.925150138 Solving -0.5416666665 + x = -0.925150138 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5416666665' to each side of the equation. -0.5416666665 + 0.5416666665 + x = -0.925150138 + 0.5416666665 Combine like terms: -0.5416666665 + 0.5416666665 = 0.0000000000 0.0000000000 + x = -0.925150138 + 0.5416666665 x = -0.925150138 + 0.5416666665 Combine like terms: -0.925150138 + 0.5416666665 = -0.3834834715 x = -0.3834834715 Simplifying x = -0.3834834715Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4668168045, -0.3834834715}
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