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Simplifying 10x + 18 = 3x2 Reorder the terms: 18 + 10x = 3x2 Solving 18 + 10x = 3x2 Solving for variable 'x'. Combine like terms: 3x2 + -3x2 = 0 18 + 10x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -6 + -3.333333333x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -3.333333333x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -3.333333333x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -3.333333333x + x2 = 0 + 6 -3.333333333x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -3.333333333x + x2 = 6 The x term is -3.333333333x. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333x + 2.777777779 + x2 = 6 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333x + x2 = 6 + 2.777777779 Combine like terms: 6 + 2.777777779 = 8.777777779 2.777777779 + -3.333333333x + x2 = 8.777777779 Factor a perfect square on the left side: (x + -1.666666667)(x + -1.666666667) = 8.777777779 Calculate the square root of the right side: 2.962731473 Break this problem into two subproblems by setting (x + -1.666666667) equal to 2.962731473 and -2.962731473.Subproblem 1
x + -1.666666667 = 2.962731473 Simplifying x + -1.666666667 = 2.962731473 Reorder the terms: -1.666666667 + x = 2.962731473 Solving -1.666666667 + x = 2.962731473 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = 2.962731473 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = 2.962731473 + 1.666666667 x = 2.962731473 + 1.666666667 Combine like terms: 2.962731473 + 1.666666667 = 4.62939814 x = 4.62939814 Simplifying x = 4.62939814Subproblem 2
x + -1.666666667 = -2.962731473 Simplifying x + -1.666666667 = -2.962731473 Reorder the terms: -1.666666667 + x = -2.962731473 Solving -1.666666667 + x = -2.962731473 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = -2.962731473 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = -2.962731473 + 1.666666667 x = -2.962731473 + 1.666666667 Combine like terms: -2.962731473 + 1.666666667 = -1.296064806 x = -1.296064806 Simplifying x = -1.296064806Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.62939814, -1.296064806}
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