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Simplifying x2 + 134x + 525 = 714 Reorder the terms: 525 + 134x + x2 = 714 Solving 525 + 134x + x2 = 714 Solving for variable 'x'. Reorder the terms: 525 + -714 + 134x + x2 = 714 + -714 Combine like terms: 525 + -714 = -189 -189 + 134x + x2 = 714 + -714 Combine like terms: 714 + -714 = 0 -189 + 134x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '189' to each side of the equation. -189 + 134x + 189 + x2 = 0 + 189 Reorder the terms: -189 + 189 + 134x + x2 = 0 + 189 Combine like terms: -189 + 189 = 0 0 + 134x + x2 = 0 + 189 134x + x2 = 0 + 189 Combine like terms: 0 + 189 = 189 134x + x2 = 189 The x term is 134x. Take half its coefficient (67). Square it (4489) and add it to both sides. Add '4489' to each side of the equation. 134x + 4489 + x2 = 189 + 4489 Reorder the terms: 4489 + 134x + x2 = 189 + 4489 Combine like terms: 189 + 4489 = 4678 4489 + 134x + x2 = 4678 Factor a perfect square on the left side: (x + 67)(x + 67) = 4678 Calculate the square root of the right side: 68.39590631 Break this problem into two subproblems by setting (x + 67) equal to 68.39590631 and -68.39590631.Subproblem 1
x + 67 = 68.39590631 Simplifying x + 67 = 68.39590631 Reorder the terms: 67 + x = 68.39590631 Solving 67 + x = 68.39590631 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-67' to each side of the equation. 67 + -67 + x = 68.39590631 + -67 Combine like terms: 67 + -67 = 0 0 + x = 68.39590631 + -67 x = 68.39590631 + -67 Combine like terms: 68.39590631 + -67 = 1.39590631 x = 1.39590631 Simplifying x = 1.39590631Subproblem 2
x + 67 = -68.39590631 Simplifying x + 67 = -68.39590631 Reorder the terms: 67 + x = -68.39590631 Solving 67 + x = -68.39590631 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-67' to each side of the equation. 67 + -67 + x = -68.39590631 + -67 Combine like terms: 67 + -67 = 0 0 + x = -68.39590631 + -67 x = -68.39590631 + -67 Combine like terms: -68.39590631 + -67 = -135.39590631 x = -135.39590631 Simplifying x = -135.39590631Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.39590631, -135.39590631}
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