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Simplifying 150 + 36x + -4.5x2 = 0 Solving 150 + 36x + -4.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.5 the coefficient of the squared term: Divide each side by '-4.5'. -33.33333333 + -8x + x2 = 0 Move the constant term to the right: Add '33.33333333' to each side of the equation. -33.33333333 + -8x + 33.33333333 + x2 = 0 + 33.33333333 Reorder the terms: -33.33333333 + 33.33333333 + -8x + x2 = 0 + 33.33333333 Combine like terms: -33.33333333 + 33.33333333 = 0.00000000 0.00000000 + -8x + x2 = 0 + 33.33333333 -8x + x2 = 0 + 33.33333333 Combine like terms: 0 + 33.33333333 = 33.33333333 -8x + x2 = 33.33333333 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 33.33333333 + 16 Reorder the terms: 16 + -8x + x2 = 33.33333333 + 16 Combine like terms: 33.33333333 + 16 = 49.33333333 16 + -8x + x2 = 49.33333333 Factor a perfect square on the left side: (x + -4)(x + -4) = 49.33333333 Calculate the square root of the right side: 7.023769168 Break this problem into two subproblems by setting (x + -4) equal to 7.023769168 and -7.023769168.Subproblem 1
x + -4 = 7.023769168 Simplifying x + -4 = 7.023769168 Reorder the terms: -4 + x = 7.023769168 Solving -4 + x = 7.023769168 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 7.023769168 + 4 Combine like terms: -4 + 4 = 0 0 + x = 7.023769168 + 4 x = 7.023769168 + 4 Combine like terms: 7.023769168 + 4 = 11.023769168 x = 11.023769168 Simplifying x = 11.023769168Subproblem 2
x + -4 = -7.023769168 Simplifying x + -4 = -7.023769168 Reorder the terms: -4 + x = -7.023769168 Solving -4 + x = -7.023769168 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -7.023769168 + 4 Combine like terms: -4 + 4 = 0 0 + x = -7.023769168 + 4 x = -7.023769168 + 4 Combine like terms: -7.023769168 + 4 = -3.023769168 x = -3.023769168 Simplifying x = -3.023769168Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.023769168, -3.023769168}
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