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Simplifying 5x2 = 36x + 18 Reorder the terms: 5x2 = 18 + 36x Solving 5x2 = 18 + 36x Solving for variable 'x'. Reorder the terms: -18 + -36x + 5x2 = 18 + 36x + -18 + -36x Reorder the terms: -18 + -36x + 5x2 = 18 + -18 + 36x + -36x Combine like terms: 18 + -18 = 0 -18 + -36x + 5x2 = 0 + 36x + -36x -18 + -36x + 5x2 = 36x + -36x Combine like terms: 36x + -36x = 0 -18 + -36x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.6 + -7.2x + x2 = 0 Move the constant term to the right: Add '3.6' to each side of the equation. -3.6 + -7.2x + 3.6 + x2 = 0 + 3.6 Reorder the terms: -3.6 + 3.6 + -7.2x + x2 = 0 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + -7.2x + x2 = 0 + 3.6 -7.2x + x2 = 0 + 3.6 Combine like terms: 0 + 3.6 = 3.6 -7.2x + x2 = 3.6 The x term is -7.2x. Take half its coefficient (-3.6). Square it (12.96) and add it to both sides. Add '12.96' to each side of the equation. -7.2x + 12.96 + x2 = 3.6 + 12.96 Reorder the terms: 12.96 + -7.2x + x2 = 3.6 + 12.96 Combine like terms: 3.6 + 12.96 = 16.56 12.96 + -7.2x + x2 = 16.56 Factor a perfect square on the left side: (x + -3.6)(x + -3.6) = 16.56 Calculate the square root of the right side: 4.06939799 Break this problem into two subproblems by setting (x + -3.6) equal to 4.06939799 and -4.06939799.Subproblem 1
x + -3.6 = 4.06939799 Simplifying x + -3.6 = 4.06939799 Reorder the terms: -3.6 + x = 4.06939799 Solving -3.6 + x = 4.06939799 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + x = 4.06939799 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + x = 4.06939799 + 3.6 x = 4.06939799 + 3.6 Combine like terms: 4.06939799 + 3.6 = 7.66939799 x = 7.66939799 Simplifying x = 7.66939799Subproblem 2
x + -3.6 = -4.06939799 Simplifying x + -3.6 = -4.06939799 Reorder the terms: -3.6 + x = -4.06939799 Solving -3.6 + x = -4.06939799 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + x = -4.06939799 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + x = -4.06939799 + 3.6 x = -4.06939799 + 3.6 Combine like terms: -4.06939799 + 3.6 = -0.46939799 x = -0.46939799 Simplifying x = -0.46939799Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.66939799, -0.46939799}
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