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Simplifying x2 + 34x = 93 Reorder the terms: 34x + x2 = 93 Solving 34x + x2 = 93 Solving for variable 'x'. Reorder the terms: -93 + 34x + x2 = 93 + -93 Combine like terms: 93 + -93 = 0 -93 + 34x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '93' to each side of the equation. -93 + 34x + 93 + x2 = 0 + 93 Reorder the terms: -93 + 93 + 34x + x2 = 0 + 93 Combine like terms: -93 + 93 = 0 0 + 34x + x2 = 0 + 93 34x + x2 = 0 + 93 Combine like terms: 0 + 93 = 93 34x + x2 = 93 The x term is 34x. Take half its coefficient (17). Square it (289) and add it to both sides. Add '289' to each side of the equation. 34x + 289 + x2 = 93 + 289 Reorder the terms: 289 + 34x + x2 = 93 + 289 Combine like terms: 93 + 289 = 382 289 + 34x + x2 = 382 Factor a perfect square on the left side: (x + 17)(x + 17) = 382 Calculate the square root of the right side: 19.544820286 Break this problem into two subproblems by setting (x + 17) equal to 19.544820286 and -19.544820286.Subproblem 1
x + 17 = 19.544820286 Simplifying x + 17 = 19.544820286 Reorder the terms: 17 + x = 19.544820286 Solving 17 + x = 19.544820286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + x = 19.544820286 + -17 Combine like terms: 17 + -17 = 0 0 + x = 19.544820286 + -17 x = 19.544820286 + -17 Combine like terms: 19.544820286 + -17 = 2.544820286 x = 2.544820286 Simplifying x = 2.544820286Subproblem 2
x + 17 = -19.544820286 Simplifying x + 17 = -19.544820286 Reorder the terms: 17 + x = -19.544820286 Solving 17 + x = -19.544820286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + x = -19.544820286 + -17 Combine like terms: 17 + -17 = 0 0 + x = -19.544820286 + -17 x = -19.544820286 + -17 Combine like terms: -19.544820286 + -17 = -36.544820286 x = -36.544820286 Simplifying x = -36.544820286Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.544820286, -36.544820286}
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