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Simplifying x2 + 34x + 53 = 0 Reorder the terms: 53 + 34x + x2 = 0 Solving 53 + 34x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-53' to each side of the equation. 53 + 34x + -53 + x2 = 0 + -53 Reorder the terms: 53 + -53 + 34x + x2 = 0 + -53 Combine like terms: 53 + -53 = 0 0 + 34x + x2 = 0 + -53 34x + x2 = 0 + -53 Combine like terms: 0 + -53 = -53 34x + x2 = -53 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 = -53 + 289 Reorder the terms: 289 + 34x + x2 = -53 + 289 Combine like terms: -53 + 289 = 236 289 + 34x + x2 = 236 Factor a perfect square on the left side: (x + 17)(x + 17) = 236 Calculate the square root of the right side: 15.362291496 Break this problem into two subproblems by setting (x + 17) equal to 15.362291496 and -15.362291496.Subproblem 1
x + 17 = 15.362291496 Simplifying x + 17 = 15.362291496 Reorder the terms: 17 + x = 15.362291496 Solving 17 + x = 15.362291496 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 = 15.362291496 + -17 Combine like terms: 17 + -17 = 0 0 + x = 15.362291496 + -17 x = 15.362291496 + -17 Combine like terms: 15.362291496 + -17 = -1.637708504 x = -1.637708504 Simplifying x = -1.637708504Subproblem 2
x + 17 = -15.362291496 Simplifying x + 17 = -15.362291496 Reorder the terms: 17 + x = -15.362291496 Solving 17 + x = -15.362291496 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 = -15.362291496 + -17 Combine like terms: 17 + -17 = 0 0 + x = -15.362291496 + -17 x = -15.362291496 + -17 Combine like terms: -15.362291496 + -17 = -32.362291496 x = -32.362291496 Simplifying x = -32.362291496Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.637708504, -32.362291496}
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