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Simplifying x2 + 14x + -311 = 0 Reorder the terms: -311 + 14x + x2 = 0 Solving -311 + 14x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '311' to each side of the equation. -311 + 14x + 311 + x2 = 0 + 311 Reorder the terms: -311 + 311 + 14x + x2 = 0 + 311 Combine like terms: -311 + 311 = 0 0 + 14x + x2 = 0 + 311 14x + x2 = 0 + 311 Combine like terms: 0 + 311 = 311 14x + x2 = 311 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 311 + 49 Reorder the terms: 49 + 14x + x2 = 311 + 49 Combine like terms: 311 + 49 = 360 49 + 14x + x2 = 360 Factor a perfect square on the left side: (x + 7)(x + 7) = 360 Calculate the square root of the right side: 18.973665961 Break this problem into two subproblems by setting (x + 7) equal to 18.973665961 and -18.973665961.Subproblem 1
x + 7 = 18.973665961 Simplifying x + 7 = 18.973665961 Reorder the terms: 7 + x = 18.973665961 Solving 7 + x = 18.973665961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 18.973665961 + -7 Combine like terms: 7 + -7 = 0 0 + x = 18.973665961 + -7 x = 18.973665961 + -7 Combine like terms: 18.973665961 + -7 = 11.973665961 x = 11.973665961 Simplifying x = 11.973665961Subproblem 2
x + 7 = -18.973665961 Simplifying x + 7 = -18.973665961 Reorder the terms: 7 + x = -18.973665961 Solving 7 + x = -18.973665961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -18.973665961 + -7 Combine like terms: 7 + -7 = 0 0 + x = -18.973665961 + -7 x = -18.973665961 + -7 Combine like terms: -18.973665961 + -7 = -25.973665961 x = -25.973665961 Simplifying x = -25.973665961Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.973665961, -25.973665961}
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