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Simplifying x * x + -14x + -52 = 0 Multiply x * x x2 + -14x + -52 = 0 Reorder the terms: -52 + -14x + x2 = 0 Solving -52 + -14x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '52' to each side of the equation. -52 + -14x + 52 + x2 = 0 + 52 Reorder the terms: -52 + 52 + -14x + x2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + -14x + x2 = 0 + 52 -14x + x2 = 0 + 52 Combine like terms: 0 + 52 = 52 -14x + x2 = 52 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 = 52 + 49 Reorder the terms: 49 + -14x + x2 = 52 + 49 Combine like terms: 52 + 49 = 101 49 + -14x + x2 = 101 Factor a perfect square on the left side: (x + -7)(x + -7) = 101 Calculate the square root of the right side: 10.049875621 Break this problem into two subproblems by setting (x + -7) equal to 10.049875621 and -10.049875621.Subproblem 1
x + -7 = 10.049875621 Simplifying x + -7 = 10.049875621 Reorder the terms: -7 + x = 10.049875621 Solving -7 + x = 10.049875621 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 = 10.049875621 + 7 Combine like terms: -7 + 7 = 0 0 + x = 10.049875621 + 7 x = 10.049875621 + 7 Combine like terms: 10.049875621 + 7 = 17.049875621 x = 17.049875621 Simplifying x = 17.049875621Subproblem 2
x + -7 = -10.049875621 Simplifying x + -7 = -10.049875621 Reorder the terms: -7 + x = -10.049875621 Solving -7 + x = -10.049875621 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 = -10.049875621 + 7 Combine like terms: -7 + 7 = 0 0 + x = -10.049875621 + 7 x = -10.049875621 + 7 Combine like terms: -10.049875621 + 7 = -3.049875621 x = -3.049875621 Simplifying x = -3.049875621Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.049875621, -3.049875621}
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