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Simplifying (3x + 2) * x = 300 Reorder the terms: (2 + 3x) * x = 300 Reorder the terms for easier multiplication: x(2 + 3x) = 300 (2 * x + 3x * x) = 300 (2x + 3x2) = 300 Solving 2x + 3x2 = 300 Solving for variable 'x'. Reorder the terms: -300 + 2x + 3x2 = 300 + -300 Combine like terms: 300 + -300 = 0 -300 + 2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -100 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + 0.6666666667x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 0.6666666667x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 0.6666666667x + x2 = 0 + 100 0.6666666667x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 0.6666666667x + x2 = 100 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 = 100 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 100 + 0.1111111112 Combine like terms: 100 + 0.1111111112 = 100.1111111112 0.1111111112 + 0.6666666667x + x2 = 100.1111111112 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 100.1111111112 Calculate the square root of the right side: 10.005554013 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 10.005554013 and -10.005554013.Subproblem 1
x + 0.3333333334 = 10.005554013 Simplifying x + 0.3333333334 = 10.005554013 Reorder the terms: 0.3333333334 + x = 10.005554013 Solving 0.3333333334 + x = 10.005554013 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 = 10.005554013 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 10.005554013 + -0.3333333334 x = 10.005554013 + -0.3333333334 Combine like terms: 10.005554013 + -0.3333333334 = 9.6722206796 x = 9.6722206796 Simplifying x = 9.6722206796Subproblem 2
x + 0.3333333334 = -10.005554013 Simplifying x + 0.3333333334 = -10.005554013 Reorder the terms: 0.3333333334 + x = -10.005554013 Solving 0.3333333334 + x = -10.005554013 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 = -10.005554013 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -10.005554013 + -0.3333333334 x = -10.005554013 + -0.3333333334 Combine like terms: -10.005554013 + -0.3333333334 = -10.3388873464 x = -10.3388873464 Simplifying x = -10.3388873464Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.6722206796, -10.3388873464}
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