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Simplifying 5 + -36x = 2x2 Solving 5 + -36x = 2x2 Solving for variable 'x'. Combine like terms: 2x2 + -2x2 = 0 5 + -36x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -2.5 + 18x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 18x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 18x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 18x + x2 = 0 + 2.5 18x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 18x + x2 = 2.5 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = 2.5 + 81 Reorder the terms: 81 + 18x + x2 = 2.5 + 81 Combine like terms: 2.5 + 81 = 83.5 81 + 18x + x2 = 83.5 Factor a perfect square on the left side: (x + 9)(x + 9) = 83.5 Calculate the square root of the right side: 9.137833441 Break this problem into two subproblems by setting (x + 9) equal to 9.137833441 and -9.137833441.Subproblem 1
x + 9 = 9.137833441 Simplifying x + 9 = 9.137833441 Reorder the terms: 9 + x = 9.137833441 Solving 9 + x = 9.137833441 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 9.137833441 + -9 Combine like terms: 9 + -9 = 0 0 + x = 9.137833441 + -9 x = 9.137833441 + -9 Combine like terms: 9.137833441 + -9 = 0.137833441 x = 0.137833441 Simplifying x = 0.137833441Subproblem 2
x + 9 = -9.137833441 Simplifying x + 9 = -9.137833441 Reorder the terms: 9 + x = -9.137833441 Solving 9 + x = -9.137833441 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -9.137833441 + -9 Combine like terms: 9 + -9 = 0 0 + x = -9.137833441 + -9 x = -9.137833441 + -9 Combine like terms: -9.137833441 + -9 = -18.137833441 x = -18.137833441 Simplifying x = -18.137833441Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.137833441, -18.137833441}
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