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Simplifying 5 = 4.6x2 + -0.5x Reorder the terms: 5 = -0.5x + 4.6x2 Solving 5 = -0.5x + 4.6x2 Solving for variable 'x'. Reorder the terms: 5 + 0.5x + -4.6x2 = -0.5x + 0.5x + 4.6x2 + -4.6x2 Combine like terms: -0.5x + 0.5x = 0.0 5 + 0.5x + -4.6x2 = 0.0 + 4.6x2 + -4.6x2 5 + 0.5x + -4.6x2 = 4.6x2 + -4.6x2 Combine like terms: 4.6x2 + -4.6x2 = 0.0 5 + 0.5x + -4.6x2 = 0.0 Begin completing the square. Divide all terms by -4.6 the coefficient of the squared term: Divide each side by '-4.6'. -1.086956522 + -0.1086956522x + x2 = 0 Move the constant term to the right: Add '1.086956522' to each side of the equation. -1.086956522 + -0.1086956522x + 1.086956522 + x2 = 0 + 1.086956522 Reorder the terms: -1.086956522 + 1.086956522 + -0.1086956522x + x2 = 0 + 1.086956522 Combine like terms: -1.086956522 + 1.086956522 = 0.000000000 0.000000000 + -0.1086956522x + x2 = 0 + 1.086956522 -0.1086956522x + x2 = 0 + 1.086956522 Combine like terms: 0 + 1.086956522 = 1.086956522 -0.1086956522x + x2 = 1.086956522 The x term is -0.1086956522x. Take half its coefficient (-0.0543478261). Square it (0.002953686202) and add it to both sides. Add '0.002953686202' to each side of the equation. -0.1086956522x + 0.002953686202 + x2 = 1.086956522 + 0.002953686202 Reorder the terms: 0.002953686202 + -0.1086956522x + x2 = 1.086956522 + 0.002953686202 Combine like terms: 1.086956522 + 0.002953686202 = 1.089910208202 0.002953686202 + -0.1086956522x + x2 = 1.089910208202 Factor a perfect square on the left side: (x + -0.0543478261)(x + -0.0543478261) = 1.089910208202 Calculate the square root of the right side: 1.043987648 Break this problem into two subproblems by setting (x + -0.0543478261) equal to 1.043987648 and -1.043987648.Subproblem 1
x + -0.0543478261 = 1.043987648 Simplifying x + -0.0543478261 = 1.043987648 Reorder the terms: -0.0543478261 + x = 1.043987648 Solving -0.0543478261 + x = 1.043987648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0543478261' to each side of the equation. -0.0543478261 + 0.0543478261 + x = 1.043987648 + 0.0543478261 Combine like terms: -0.0543478261 + 0.0543478261 = 0.0000000000 0.0000000000 + x = 1.043987648 + 0.0543478261 x = 1.043987648 + 0.0543478261 Combine like terms: 1.043987648 + 0.0543478261 = 1.0983354741 x = 1.0983354741 Simplifying x = 1.0983354741Subproblem 2
x + -0.0543478261 = -1.043987648 Simplifying x + -0.0543478261 = -1.043987648 Reorder the terms: -0.0543478261 + x = -1.043987648 Solving -0.0543478261 + x = -1.043987648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0543478261' to each side of the equation. -0.0543478261 + 0.0543478261 + x = -1.043987648 + 0.0543478261 Combine like terms: -0.0543478261 + 0.0543478261 = 0.0000000000 0.0000000000 + x = -1.043987648 + 0.0543478261 x = -1.043987648 + 0.0543478261 Combine like terms: -1.043987648 + 0.0543478261 = -0.9896398219 x = -0.9896398219 Simplifying x = -0.9896398219Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0983354741, -0.9896398219}
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