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Simplifying x2 + 14x = 282 Reorder the terms: 14x + x2 = 282 Solving 14x + x2 = 282 Solving for variable 'x'. Reorder the terms: -282 + 14x + x2 = 282 + -282 Combine like terms: 282 + -282 = 0 -282 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '282' to each side of the equation. -282 + 14x + 282 + x2 = 0 + 282 Reorder the terms: -282 + 282 + 14x + x2 = 0 + 282 Combine like terms: -282 + 282 = 0 0 + 14x + x2 = 0 + 282 14x + x2 = 0 + 282 Combine like terms: 0 + 282 = 282 14x + x2 = 282 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 = 282 + 49 Reorder the terms: 49 + 14x + x2 = 282 + 49 Combine like terms: 282 + 49 = 331 49 + 14x + x2 = 331 Factor a perfect square on the left side: (x + 7)(x + 7) = 331 Calculate the square root of the right side: 18.193405399 Break this problem into two subproblems by setting (x + 7) equal to 18.193405399 and -18.193405399.Subproblem 1
x + 7 = 18.193405399 Simplifying x + 7 = 18.193405399 Reorder the terms: 7 + x = 18.193405399 Solving 7 + x = 18.193405399 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 = 18.193405399 + -7 Combine like terms: 7 + -7 = 0 0 + x = 18.193405399 + -7 x = 18.193405399 + -7 Combine like terms: 18.193405399 + -7 = 11.193405399 x = 11.193405399 Simplifying x = 11.193405399Subproblem 2
x + 7 = -18.193405399 Simplifying x + 7 = -18.193405399 Reorder the terms: 7 + x = -18.193405399 Solving 7 + x = -18.193405399 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 = -18.193405399 + -7 Combine like terms: 7 + -7 = 0 0 + x = -18.193405399 + -7 x = -18.193405399 + -7 Combine like terms: -18.193405399 + -7 = -25.193405399 x = -25.193405399 Simplifying x = -25.193405399Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.193405399, -25.193405399}
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