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Simplifying 10 = x2 + -4.06x Reorder the terms: 10 = -4.06x + x2 Solving 10 = -4.06x + x2 Solving for variable 'x'. Reorder the terms: 10 + 4.06x + -1x2 = -4.06x + 4.06x + x2 + -1x2 Combine like terms: -4.06x + 4.06x = 0.00 10 + 4.06x + -1x2 = 0.00 + x2 + -1x2 10 + 4.06x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 10 + 4.06x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -10 + -4.06x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -4.06x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -4.06x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -4.06x + x2 = 0 + 10 -4.06x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -4.06x + x2 = 10 The x term is -4.06x. Take half its coefficient (-2.03). Square it (4.1209) and add it to both sides. Add '4.1209' to each side of the equation. -4.06x + 4.1209 + x2 = 10 + 4.1209 Reorder the terms: 4.1209 + -4.06x + x2 = 10 + 4.1209 Combine like terms: 10 + 4.1209 = 14.1209 4.1209 + -4.06x + x2 = 14.1209 Factor a perfect square on the left side: (x + -2.03)(x + -2.03) = 14.1209 Calculate the square root of the right side: 3.757778599 Break this problem into two subproblems by setting (x + -2.03) equal to 3.757778599 and -3.757778599.Subproblem 1
x + -2.03 = 3.757778599 Simplifying x + -2.03 = 3.757778599 Reorder the terms: -2.03 + x = 3.757778599 Solving -2.03 + x = 3.757778599 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.03' to each side of the equation. -2.03 + 2.03 + x = 3.757778599 + 2.03 Combine like terms: -2.03 + 2.03 = 0.00 0.00 + x = 3.757778599 + 2.03 x = 3.757778599 + 2.03 Combine like terms: 3.757778599 + 2.03 = 5.787778599 x = 5.787778599 Simplifying x = 5.787778599Subproblem 2
x + -2.03 = -3.757778599 Simplifying x + -2.03 = -3.757778599 Reorder the terms: -2.03 + x = -3.757778599 Solving -2.03 + x = -3.757778599 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.03' to each side of the equation. -2.03 + 2.03 + x = -3.757778599 + 2.03 Combine like terms: -2.03 + 2.03 = 0.00 0.00 + x = -3.757778599 + 2.03 x = -3.757778599 + 2.03 Combine like terms: -3.757778599 + 2.03 = -1.727778599 x = -1.727778599 Simplifying x = -1.727778599Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.787778599, -1.727778599}
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