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Simplifying 2x + 3x2 = 90 Solving 2x + 3x2 = 90 Solving for variable 'x'. Reorder the terms: -90 + 2x + 3x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + 2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -30 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + 0.6666666667x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 0.6666666667x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 0.6666666667x + x2 = 0 + 30 0.6666666667x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 0.6666666667x + x2 = 30 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 = 30 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 30 + 0.1111111112 Combine like terms: 30 + 0.1111111112 = 30.1111111112 0.1111111112 + 0.6666666667x + x2 = 30.1111111112 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 30.1111111112 Calculate the square root of the right side: 5.487359211 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 5.487359211 and -5.487359211.Subproblem 1
x + 0.3333333334 = 5.487359211 Simplifying x + 0.3333333334 = 5.487359211 Reorder the terms: 0.3333333334 + x = 5.487359211 Solving 0.3333333334 + x = 5.487359211 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 = 5.487359211 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 5.487359211 + -0.3333333334 x = 5.487359211 + -0.3333333334 Combine like terms: 5.487359211 + -0.3333333334 = 5.1540258776 x = 5.1540258776 Simplifying x = 5.1540258776Subproblem 2
x + 0.3333333334 = -5.487359211 Simplifying x + 0.3333333334 = -5.487359211 Reorder the terms: 0.3333333334 + x = -5.487359211 Solving 0.3333333334 + x = -5.487359211 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 = -5.487359211 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -5.487359211 + -0.3333333334 x = -5.487359211 + -0.3333333334 Combine like terms: -5.487359211 + -0.3333333334 = -5.8206925444 x = -5.8206925444 Simplifying x = -5.8206925444Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.1540258776, -5.8206925444}
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