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Simplifying (X + -7)(X + 5) = 90 Reorder the terms: (-7 + X)(X + 5) = 90 Reorder the terms: (-7 + X)(5 + X) = 90 Multiply (-7 + X) * (5 + X) (-7(5 + X) + X(5 + X)) = 90 ((5 * -7 + X * -7) + X(5 + X)) = 90 ((-35 + -7X) + X(5 + X)) = 90 (-35 + -7X + (5 * X + X * X)) = 90 (-35 + -7X + (5X + X2)) = 90 Combine like terms: -7X + 5X = -2X (-35 + -2X + X2) = 90 Solving -35 + -2X + X2 = 90 Solving for variable 'X'. Reorder the terms: -35 + -90 + -2X + X2 = 90 + -90 Combine like terms: -35 + -90 = -125 -125 + -2X + X2 = 90 + -90 Combine like terms: 90 + -90 = 0 -125 + -2X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '125' to each side of the equation. -125 + -2X + 125 + X2 = 0 + 125 Reorder the terms: -125 + 125 + -2X + X2 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + -2X + X2 = 0 + 125 -2X + X2 = 0 + 125 Combine like terms: 0 + 125 = 125 -2X + X2 = 125 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 = 125 + 1 Reorder the terms: 1 + -2X + X2 = 125 + 1 Combine like terms: 125 + 1 = 126 1 + -2X + X2 = 126 Factor a perfect square on the left side: (X + -1)(X + -1) = 126 Calculate the square root of the right side: 11.22497216 Break this problem into two subproblems by setting (X + -1) equal to 11.22497216 and -11.22497216.Subproblem 1
X + -1 = 11.22497216 Simplifying X + -1 = 11.22497216 Reorder the terms: -1 + X = 11.22497216 Solving -1 + X = 11.22497216 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 = 11.22497216 + 1 Combine like terms: -1 + 1 = 0 0 + X = 11.22497216 + 1 X = 11.22497216 + 1 Combine like terms: 11.22497216 + 1 = 12.22497216 X = 12.22497216 Simplifying X = 12.22497216Subproblem 2
X + -1 = -11.22497216 Simplifying X + -1 = -11.22497216 Reorder the terms: -1 + X = -11.22497216 Solving -1 + X = -11.22497216 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 = -11.22497216 + 1 Combine like terms: -1 + 1 = 0 0 + X = -11.22497216 + 1 X = -11.22497216 + 1 Combine like terms: -11.22497216 + 1 = -10.22497216 X = -10.22497216 Simplifying X = -10.22497216Solution
The solution to the problem is based on the solutions from the subproblems. X = {12.22497216, -10.22497216}
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