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Simplifying x(x + 14) = 270 Reorder the terms: x(14 + x) = 270 (14 * x + x * x) = 270 (14x + x2) = 270 Solving 14x + x2 = 270 Solving for variable 'x'. Reorder the terms: -270 + 14x + x2 = 270 + -270 Combine like terms: 270 + -270 = 0 -270 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '270' to each side of the equation. -270 + 14x + 270 + x2 = 0 + 270 Reorder the terms: -270 + 270 + 14x + x2 = 0 + 270 Combine like terms: -270 + 270 = 0 0 + 14x + x2 = 0 + 270 14x + x2 = 0 + 270 Combine like terms: 0 + 270 = 270 14x + x2 = 270 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 = 270 + 49 Reorder the terms: 49 + 14x + x2 = 270 + 49 Combine like terms: 270 + 49 = 319 49 + 14x + x2 = 319 Factor a perfect square on the left side: (x + 7)(x + 7) = 319 Calculate the square root of the right side: 17.860571099 Break this problem into two subproblems by setting (x + 7) equal to 17.860571099 and -17.860571099.Subproblem 1
x + 7 = 17.860571099 Simplifying x + 7 = 17.860571099 Reorder the terms: 7 + x = 17.860571099 Solving 7 + x = 17.860571099 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 = 17.860571099 + -7 Combine like terms: 7 + -7 = 0 0 + x = 17.860571099 + -7 x = 17.860571099 + -7 Combine like terms: 17.860571099 + -7 = 10.860571099 x = 10.860571099 Simplifying x = 10.860571099Subproblem 2
x + 7 = -17.860571099 Simplifying x + 7 = -17.860571099 Reorder the terms: 7 + x = -17.860571099 Solving 7 + x = -17.860571099 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 = -17.860571099 + -7 Combine like terms: 7 + -7 = 0 0 + x = -17.860571099 + -7 x = -17.860571099 + -7 Combine like terms: -17.860571099 + -7 = -24.860571099 x = -24.860571099 Simplifying x = -24.860571099Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.860571099, -24.860571099}
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