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Simplifying x(5x + -36) = 26 Reorder the terms: x(-36 + 5x) = 26 (-36 * x + 5x * x) = 26 (-36x + 5x2) = 26 Solving -36x + 5x2 = 26 Solving for variable 'x'. Reorder the terms: -26 + -36x + 5x2 = 26 + -26 Combine like terms: 26 + -26 = 0 -26 + -36x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5.2 + -7.2x + x2 = 0 Move the constant term to the right: Add '5.2' to each side of the equation. -5.2 + -7.2x + 5.2 + x2 = 0 + 5.2 Reorder the terms: -5.2 + 5.2 + -7.2x + x2 = 0 + 5.2 Combine like terms: -5.2 + 5.2 = 0.0 0.0 + -7.2x + x2 = 0 + 5.2 -7.2x + x2 = 0 + 5.2 Combine like terms: 0 + 5.2 = 5.2 -7.2x + x2 = 5.2 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 = 5.2 + 12.96 Reorder the terms: 12.96 + -7.2x + x2 = 5.2 + 12.96 Combine like terms: 5.2 + 12.96 = 18.16 12.96 + -7.2x + x2 = 18.16 Factor a perfect square on the left side: (x + -3.6)(x + -3.6) = 18.16 Calculate the square root of the right side: 4.261455151 Break this problem into two subproblems by setting (x + -3.6) equal to 4.261455151 and -4.261455151.Subproblem 1
x + -3.6 = 4.261455151 Simplifying x + -3.6 = 4.261455151 Reorder the terms: -3.6 + x = 4.261455151 Solving -3.6 + x = 4.261455151 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 = 4.261455151 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + x = 4.261455151 + 3.6 x = 4.261455151 + 3.6 Combine like terms: 4.261455151 + 3.6 = 7.861455151 x = 7.861455151 Simplifying x = 7.861455151Subproblem 2
x + -3.6 = -4.261455151 Simplifying x + -3.6 = -4.261455151 Reorder the terms: -3.6 + x = -4.261455151 Solving -3.6 + x = -4.261455151 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 = -4.261455151 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + x = -4.261455151 + 3.6 x = -4.261455151 + 3.6 Combine like terms: -4.261455151 + 3.6 = -0.661455151 x = -0.661455151 Simplifying x = -0.661455151Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.861455151, -0.661455151}
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