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Simplifying (x + 7)(x + -3) = 90 Reorder the terms: (7 + x)(x + -3) = 90 Reorder the terms: (7 + x)(-3 + x) = 90 Multiply (7 + x) * (-3 + x) (7(-3 + x) + x(-3 + x)) = 90 ((-3 * 7 + x * 7) + x(-3 + x)) = 90 ((-21 + 7x) + x(-3 + x)) = 90 (-21 + 7x + (-3 * x + x * x)) = 90 (-21 + 7x + (-3x + x2)) = 90 Combine like terms: 7x + -3x = 4x (-21 + 4x + x2) = 90 Solving -21 + 4x + x2 = 90 Solving for variable 'x'. Reorder the terms: -21 + -90 + 4x + x2 = 90 + -90 Combine like terms: -21 + -90 = -111 -111 + 4x + x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -111 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '111' to each side of the equation. -111 + 4x + 111 + x2 = 0 + 111 Reorder the terms: -111 + 111 + 4x + x2 = 0 + 111 Combine like terms: -111 + 111 = 0 0 + 4x + x2 = 0 + 111 4x + x2 = 0 + 111 Combine like terms: 0 + 111 = 111 4x + x2 = 111 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 111 + 4 Reorder the terms: 4 + 4x + x2 = 111 + 4 Combine like terms: 111 + 4 = 115 4 + 4x + x2 = 115 Factor a perfect square on the left side: (x + 2)(x + 2) = 115 Calculate the square root of the right side: 10.723805295 Break this problem into two subproblems by setting (x + 2) equal to 10.723805295 and -10.723805295.Subproblem 1
x + 2 = 10.723805295 Simplifying x + 2 = 10.723805295 Reorder the terms: 2 + x = 10.723805295 Solving 2 + x = 10.723805295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 10.723805295 + -2 Combine like terms: 2 + -2 = 0 0 + x = 10.723805295 + -2 x = 10.723805295 + -2 Combine like terms: 10.723805295 + -2 = 8.723805295 x = 8.723805295 Simplifying x = 8.723805295Subproblem 2
x + 2 = -10.723805295 Simplifying x + 2 = -10.723805295 Reorder the terms: 2 + x = -10.723805295 Solving 2 + x = -10.723805295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -10.723805295 + -2 Combine like terms: 2 + -2 = 0 0 + x = -10.723805295 + -2 x = -10.723805295 + -2 Combine like terms: -10.723805295 + -2 = -12.723805295 x = -12.723805295 Simplifying x = -12.723805295Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.723805295, -12.723805295}
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