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Simplifying 2x + 3x2 = 666 Solving 2x + 3x2 = 666 Solving for variable 'x'. Reorder the terms: -666 + 2x + 3x2 = 666 + -666 Combine like terms: 666 + -666 = 0 -666 + 2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -222 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '222' to each side of the equation. -222 + 0.6666666667x + 222 + x2 = 0 + 222 Reorder the terms: -222 + 222 + 0.6666666667x + x2 = 0 + 222 Combine like terms: -222 + 222 = 0 0 + 0.6666666667x + x2 = 0 + 222 0.6666666667x + x2 = 0 + 222 Combine like terms: 0 + 222 = 222 0.6666666667x + x2 = 222 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 222 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 222 + 0.1111111112 Combine like terms: 222 + 0.1111111112 = 222.1111111112 0.1111111112 + 0.6666666667x + x2 = 222.1111111112 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 222.1111111112 Calculate the square root of the right side: 14.903392604 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 14.903392604 and -14.903392604.Subproblem 1
x + 0.3333333334 = 14.903392604 Simplifying x + 0.3333333334 = 14.903392604 Reorder the terms: 0.3333333334 + x = 14.903392604 Solving 0.3333333334 + x = 14.903392604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 14.903392604 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 14.903392604 + -0.3333333334 x = 14.903392604 + -0.3333333334 Combine like terms: 14.903392604 + -0.3333333334 = 14.5700592706 x = 14.5700592706 Simplifying x = 14.5700592706Subproblem 2
x + 0.3333333334 = -14.903392604 Simplifying x + 0.3333333334 = -14.903392604 Reorder the terms: 0.3333333334 + x = -14.903392604 Solving 0.3333333334 + x = -14.903392604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -14.903392604 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -14.903392604 + -0.3333333334 x = -14.903392604 + -0.3333333334 Combine like terms: -14.903392604 + -0.3333333334 = -15.2367259374 x = -15.2367259374 Simplifying x = -15.2367259374Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.5700592706, -15.2367259374}
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