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Simplifying x2 + -4.167x + 4 = 0 Reorder the terms: 4 + -4.167x + x2 = 0 Solving 4 + -4.167x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -4.167x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -4.167x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -4.167x + x2 = 0 + -4 -4.167x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -4.167x + x2 = -4 The x term is -4.167x. Take half its coefficient (-2.0835). Square it (4.34097225) and add it to both sides. Add '4.34097225' to each side of the equation. -4.167x + 4.34097225 + x2 = -4 + 4.34097225 Reorder the terms: 4.34097225 + -4.167x + x2 = -4 + 4.34097225 Combine like terms: -4 + 4.34097225 = 0.34097225 4.34097225 + -4.167x + x2 = 0.34097225 Factor a perfect square on the left side: (x + -2.0835)(x + -2.0835) = 0.34097225 Calculate the square root of the right side: 0.583928292 Break this problem into two subproblems by setting (x + -2.0835) equal to 0.583928292 and -0.583928292.Subproblem 1
x + -2.0835 = 0.583928292 Simplifying x + -2.0835 = 0.583928292 Reorder the terms: -2.0835 + x = 0.583928292 Solving -2.0835 + x = 0.583928292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.0835' to each side of the equation. -2.0835 + 2.0835 + x = 0.583928292 + 2.0835 Combine like terms: -2.0835 + 2.0835 = 0.0000 0.0000 + x = 0.583928292 + 2.0835 x = 0.583928292 + 2.0835 Combine like terms: 0.583928292 + 2.0835 = 2.667428292 x = 2.667428292 Simplifying x = 2.667428292Subproblem 2
x + -2.0835 = -0.583928292 Simplifying x + -2.0835 = -0.583928292 Reorder the terms: -2.0835 + x = -0.583928292 Solving -2.0835 + x = -0.583928292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.0835' to each side of the equation. -2.0835 + 2.0835 + x = -0.583928292 + 2.0835 Combine like terms: -2.0835 + 2.0835 = 0.0000 0.0000 + x = -0.583928292 + 2.0835 x = -0.583928292 + 2.0835 Combine like terms: -0.583928292 + 2.0835 = 1.499571708 x = 1.499571708 Simplifying x = 1.499571708Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.667428292, 1.499571708}
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