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Simplifying 2x2 + 36x = 51 Reorder the terms: 36x + 2x2 = 51 Solving 36x + 2x2 = 51 Solving for variable 'x'. Reorder the terms: -51 + 36x + 2x2 = 51 + -51 Combine like terms: 51 + -51 = 0 -51 + 36x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -25.5 + 18x + x2 = 0 Move the constant term to the right: Add '25.5' to each side of the equation. -25.5 + 18x + 25.5 + x2 = 0 + 25.5 Reorder the terms: -25.5 + 25.5 + 18x + x2 = 0 + 25.5 Combine like terms: -25.5 + 25.5 = 0.0 0.0 + 18x + x2 = 0 + 25.5 18x + x2 = 0 + 25.5 Combine like terms: 0 + 25.5 = 25.5 18x + x2 = 25.5 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 = 25.5 + 81 Reorder the terms: 81 + 18x + x2 = 25.5 + 81 Combine like terms: 25.5 + 81 = 106.5 81 + 18x + x2 = 106.5 Factor a perfect square on the left side: (x + 9)(x + 9) = 106.5 Calculate the square root of the right side: 10.31988372 Break this problem into two subproblems by setting (x + 9) equal to 10.31988372 and -10.31988372.Subproblem 1
x + 9 = 10.31988372 Simplifying x + 9 = 10.31988372 Reorder the terms: 9 + x = 10.31988372 Solving 9 + x = 10.31988372 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 = 10.31988372 + -9 Combine like terms: 9 + -9 = 0 0 + x = 10.31988372 + -9 x = 10.31988372 + -9 Combine like terms: 10.31988372 + -9 = 1.31988372 x = 1.31988372 Simplifying x = 1.31988372Subproblem 2
x + 9 = -10.31988372 Simplifying x + 9 = -10.31988372 Reorder the terms: 9 + x = -10.31988372 Solving 9 + x = -10.31988372 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 = -10.31988372 + -9 Combine like terms: 9 + -9 = 0 0 + x = -10.31988372 + -9 x = -10.31988372 + -9 Combine like terms: -10.31988372 + -9 = -19.31988372 x = -19.31988372 Simplifying x = -19.31988372Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.31988372, -19.31988372}
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