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Simplifying 6x2 + 9x = 362 Reorder the terms: 9x + 6x2 = 362 Solving 9x + 6x2 = 362 Solving for variable 'x'. Reorder the terms: -362 + 9x + 6x2 = 362 + -362 Combine like terms: 362 + -362 = 0 -362 + 9x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -60.33333333 + 1.5x + x2 = 0 Move the constant term to the right: Add '60.33333333' to each side of the equation. -60.33333333 + 1.5x + 60.33333333 + x2 = 0 + 60.33333333 Reorder the terms: -60.33333333 + 60.33333333 + 1.5x + x2 = 0 + 60.33333333 Combine like terms: -60.33333333 + 60.33333333 = 0.00000000 0.00000000 + 1.5x + x2 = 0 + 60.33333333 1.5x + x2 = 0 + 60.33333333 Combine like terms: 0 + 60.33333333 = 60.33333333 1.5x + x2 = 60.33333333 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 60.33333333 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 60.33333333 + 0.5625 Combine like terms: 60.33333333 + 0.5625 = 60.89583333 0.5625 + 1.5x + x2 = 60.89583333 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 60.89583333 Calculate the square root of the right side: 7.803578239 Break this problem into two subproblems by setting (x + 0.75) equal to 7.803578239 and -7.803578239.Subproblem 1
x + 0.75 = 7.803578239 Simplifying x + 0.75 = 7.803578239 Reorder the terms: 0.75 + x = 7.803578239 Solving 0.75 + x = 7.803578239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 7.803578239 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 7.803578239 + -0.75 x = 7.803578239 + -0.75 Combine like terms: 7.803578239 + -0.75 = 7.053578239 x = 7.053578239 Simplifying x = 7.053578239Subproblem 2
x + 0.75 = -7.803578239 Simplifying x + 0.75 = -7.803578239 Reorder the terms: 0.75 + x = -7.803578239 Solving 0.75 + x = -7.803578239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -7.803578239 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -7.803578239 + -0.75 x = -7.803578239 + -0.75 Combine like terms: -7.803578239 + -0.75 = -8.553578239 x = -8.553578239 Simplifying x = -8.553578239Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.053578239, -8.553578239}
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