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Simplifying x2 + -14x + 49 = 283 Reorder the terms: 49 + -14x + x2 = 283 Solving 49 + -14x + x2 = 283 Solving for variable 'x'. Reorder the terms: 49 + -283 + -14x + x2 = 283 + -283 Combine like terms: 49 + -283 = -234 -234 + -14x + x2 = 283 + -283 Combine like terms: 283 + -283 = 0 -234 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '234' to each side of the equation. -234 + -14x + 234 + x2 = 0 + 234 Reorder the terms: -234 + 234 + -14x + x2 = 0 + 234 Combine like terms: -234 + 234 = 0 0 + -14x + x2 = 0 + 234 -14x + x2 = 0 + 234 Combine like terms: 0 + 234 = 234 -14x + x2 = 234 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 = 234 + 49 Reorder the terms: 49 + -14x + x2 = 234 + 49 Combine like terms: 234 + 49 = 283 49 + -14x + x2 = 283 Factor a perfect square on the left side: (x + -7)(x + -7) = 283 Calculate the square root of the right side: 16.822603841 Break this problem into two subproblems by setting (x + -7) equal to 16.822603841 and -16.822603841.Subproblem 1
x + -7 = 16.822603841 Simplifying x + -7 = 16.822603841 Reorder the terms: -7 + x = 16.822603841 Solving -7 + x = 16.822603841 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 = 16.822603841 + 7 Combine like terms: -7 + 7 = 0 0 + x = 16.822603841 + 7 x = 16.822603841 + 7 Combine like terms: 16.822603841 + 7 = 23.822603841 x = 23.822603841 Simplifying x = 23.822603841Subproblem 2
x + -7 = -16.822603841 Simplifying x + -7 = -16.822603841 Reorder the terms: -7 + x = -16.822603841 Solving -7 + x = -16.822603841 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 = -16.822603841 + 7 Combine like terms: -7 + 7 = 0 0 + x = -16.822603841 + 7 x = -16.822603841 + 7 Combine like terms: -16.822603841 + 7 = -9.822603841 x = -9.822603841 Simplifying x = -9.822603841Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.822603841, -9.822603841}
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