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Simplifying 3x2 + 2x + 3 = 297 Reorder the terms: 3 + 2x + 3x2 = 297 Solving 3 + 2x + 3x2 = 297 Solving for variable 'x'. Reorder the terms: 3 + -297 + 2x + 3x2 = 297 + -297 Combine like terms: 3 + -297 = -294 -294 + 2x + 3x2 = 297 + -297 Combine like terms: 297 + -297 = 0 -294 + 2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -98 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '98' to each side of the equation. -98 + 0.6666666667x + 98 + x2 = 0 + 98 Reorder the terms: -98 + 98 + 0.6666666667x + x2 = 0 + 98 Combine like terms: -98 + 98 = 0 0 + 0.6666666667x + x2 = 0 + 98 0.6666666667x + x2 = 0 + 98 Combine like terms: 0 + 98 = 98 0.6666666667x + x2 = 98 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 = 98 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 98 + 0.1111111112 Combine like terms: 98 + 0.1111111112 = 98.1111111112 0.1111111112 + 0.6666666667x + x2 = 98.1111111112 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 98.1111111112 Calculate the square root of the right side: 9.905105305 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 9.905105305 and -9.905105305.Subproblem 1
x + 0.3333333334 = 9.905105305 Simplifying x + 0.3333333334 = 9.905105305 Reorder the terms: 0.3333333334 + x = 9.905105305 Solving 0.3333333334 + x = 9.905105305 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 = 9.905105305 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 9.905105305 + -0.3333333334 x = 9.905105305 + -0.3333333334 Combine like terms: 9.905105305 + -0.3333333334 = 9.5717719716 x = 9.5717719716 Simplifying x = 9.5717719716Subproblem 2
x + 0.3333333334 = -9.905105305 Simplifying x + 0.3333333334 = -9.905105305 Reorder the terms: 0.3333333334 + x = -9.905105305 Solving 0.3333333334 + x = -9.905105305 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 = -9.905105305 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -9.905105305 + -0.3333333334 x = -9.905105305 + -0.3333333334 Combine like terms: -9.905105305 + -0.3333333334 = -10.2384386384 x = -10.2384386384 Simplifying x = -10.2384386384Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.5717719716, -10.2384386384}
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