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Simplifying (x)(x) + -2x + -60 = -7 Multiply x * x x2 + -2x + -60 = -7 Reorder the terms: -60 + -2x + x2 = -7 Solving -60 + -2x + x2 = -7 Solving for variable 'x'. Reorder the terms: -60 + 7 + -2x + x2 = -7 + 7 Combine like terms: -60 + 7 = -53 -53 + -2x + x2 = -7 + 7 Combine like terms: -7 + 7 = 0 -53 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '53' to each side of the equation. -53 + -2x + 53 + x2 = 0 + 53 Reorder the terms: -53 + 53 + -2x + x2 = 0 + 53 Combine like terms: -53 + 53 = 0 0 + -2x + x2 = 0 + 53 -2x + x2 = 0 + 53 Combine like terms: 0 + 53 = 53 -2x + x2 = 53 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 53 + 1 Reorder the terms: 1 + -2x + x2 = 53 + 1 Combine like terms: 53 + 1 = 54 1 + -2x + x2 = 54 Factor a perfect square on the left side: (x + -1)(x + -1) = 54 Calculate the square root of the right side: 7.348469228 Break this problem into two subproblems by setting (x + -1) equal to 7.348469228 and -7.348469228.Subproblem 1
x + -1 = 7.348469228 Simplifying x + -1 = 7.348469228 Reorder the terms: -1 + x = 7.348469228 Solving -1 + x = 7.348469228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 7.348469228 + 1 Combine like terms: -1 + 1 = 0 0 + x = 7.348469228 + 1 x = 7.348469228 + 1 Combine like terms: 7.348469228 + 1 = 8.348469228 x = 8.348469228 Simplifying x = 8.348469228Subproblem 2
x + -1 = -7.348469228 Simplifying x + -1 = -7.348469228 Reorder the terms: -1 + x = -7.348469228 Solving -1 + x = -7.348469228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -7.348469228 + 1 Combine like terms: -1 + 1 = 0 0 + x = -7.348469228 + 1 x = -7.348469228 + 1 Combine like terms: -7.348469228 + 1 = -6.348469228 x = -6.348469228 Simplifying x = -6.348469228Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.348469228, -6.348469228}
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