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Simplifying x2 + 34x + 7 = 0 Reorder the terms: 7 + 34x + x2 = 0 Solving 7 + 34x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 34x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + 34x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 34x + x2 = 0 + -7 34x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 34x + x2 = -7 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 = -7 + 289 Reorder the terms: 289 + 34x + x2 = -7 + 289 Combine like terms: -7 + 289 = 282 289 + 34x + x2 = 282 Factor a perfect square on the left side: (x + 17)(x + 17) = 282 Calculate the square root of the right side: 16.792855624 Break this problem into two subproblems by setting (x + 17) equal to 16.792855624 and -16.792855624.Subproblem 1
x + 17 = 16.792855624 Simplifying x + 17 = 16.792855624 Reorder the terms: 17 + x = 16.792855624 Solving 17 + x = 16.792855624 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 = 16.792855624 + -17 Combine like terms: 17 + -17 = 0 0 + x = 16.792855624 + -17 x = 16.792855624 + -17 Combine like terms: 16.792855624 + -17 = -0.207144376 x = -0.207144376 Simplifying x = -0.207144376Subproblem 2
x + 17 = -16.792855624 Simplifying x + 17 = -16.792855624 Reorder the terms: 17 + x = -16.792855624 Solving 17 + x = -16.792855624 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 = -16.792855624 + -17 Combine like terms: 17 + -17 = 0 0 + x = -16.792855624 + -17 x = -16.792855624 + -17 Combine like terms: -16.792855624 + -17 = -33.792855624 x = -33.792855624 Simplifying x = -33.792855624Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.207144376, -33.792855624}
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