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Simplifying 2x2 = 30x + 27 Reorder the terms: 2x2 = 27 + 30x Solving 2x2 = 27 + 30x Solving for variable 'x'. Reorder the terms: -27 + -30x + 2x2 = 27 + 30x + -27 + -30x Reorder the terms: -27 + -30x + 2x2 = 27 + -27 + 30x + -30x Combine like terms: 27 + -27 = 0 -27 + -30x + 2x2 = 0 + 30x + -30x -27 + -30x + 2x2 = 30x + -30x Combine like terms: 30x + -30x = 0 -27 + -30x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -13.5 + -15x + x2 = 0 Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + -15x + 13.5 + x2 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + -15x + x2 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + -15x + x2 = 0 + 13.5 -15x + x2 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 -15x + x2 = 13.5 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = 13.5 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 13.5 + 56.25 Combine like terms: 13.5 + 56.25 = 69.75 56.25 + -15x + x2 = 69.75 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 69.75 Calculate the square root of the right side: 8.351646544 Break this problem into two subproblems by setting (x + -7.5) equal to 8.351646544 and -8.351646544.Subproblem 1
x + -7.5 = 8.351646544 Simplifying x + -7.5 = 8.351646544 Reorder the terms: -7.5 + x = 8.351646544 Solving -7.5 + x = 8.351646544 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 8.351646544 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 8.351646544 + 7.5 x = 8.351646544 + 7.5 Combine like terms: 8.351646544 + 7.5 = 15.851646544 x = 15.851646544 Simplifying x = 15.851646544Subproblem 2
x + -7.5 = -8.351646544 Simplifying x + -7.5 = -8.351646544 Reorder the terms: -7.5 + x = -8.351646544 Solving -7.5 + x = -8.351646544 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -8.351646544 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -8.351646544 + 7.5 x = -8.351646544 + 7.5 Combine like terms: -8.351646544 + 7.5 = -0.851646544 x = -0.851646544 Simplifying x = -0.851646544Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.851646544, -0.851646544}
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