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Simplifying (x + 7)(x + 8) = 37 Reorder the terms: (7 + x)(x + 8) = 37 Reorder the terms: (7 + x)(8 + x) = 37 Multiply (7 + x) * (8 + x) (7(8 + x) + x(8 + x)) = 37 ((8 * 7 + x * 7) + x(8 + x)) = 37 ((56 + 7x) + x(8 + x)) = 37 (56 + 7x + (8 * x + x * x)) = 37 (56 + 7x + (8x + x2)) = 37 Combine like terms: 7x + 8x = 15x (56 + 15x + x2) = 37 Solving 56 + 15x + x2 = 37 Solving for variable 'x'. Reorder the terms: 56 + -37 + 15x + x2 = 37 + -37 Combine like terms: 56 + -37 = 19 19 + 15x + x2 = 37 + -37 Combine like terms: 37 + -37 = 0 19 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + 15x + -19 + x2 = 0 + -19 Reorder the terms: 19 + -19 + 15x + x2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + 15x + x2 = 0 + -19 15x + x2 = 0 + -19 Combine like terms: 0 + -19 = -19 15x + x2 = -19 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = -19 + 56.25 Reorder the terms: 56.25 + 15x + x2 = -19 + 56.25 Combine like terms: -19 + 56.25 = 37.25 56.25 + 15x + x2 = 37.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 37.25 Calculate the square root of the right side: 6.103277808 Break this problem into two subproblems by setting (x + 7.5) equal to 6.103277808 and -6.103277808.Subproblem 1
x + 7.5 = 6.103277808 Simplifying x + 7.5 = 6.103277808 Reorder the terms: 7.5 + x = 6.103277808 Solving 7.5 + x = 6.103277808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 6.103277808 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 6.103277808 + -7.5 x = 6.103277808 + -7.5 Combine like terms: 6.103277808 + -7.5 = -1.396722192 x = -1.396722192 Simplifying x = -1.396722192Subproblem 2
x + 7.5 = -6.103277808 Simplifying x + 7.5 = -6.103277808 Reorder the terms: 7.5 + x = -6.103277808 Solving 7.5 + x = -6.103277808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -6.103277808 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -6.103277808 + -7.5 x = -6.103277808 + -7.5 Combine like terms: -6.103277808 + -7.5 = -13.603277808 x = -13.603277808 Simplifying x = -13.603277808Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.396722192, -13.603277808}
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