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Simplifying (x + 10)(x + 9) = 4 Reorder the terms: (10 + x)(x + 9) = 4 Reorder the terms: (10 + x)(9 + x) = 4 Multiply (10 + x) * (9 + x) (10(9 + x) + x(9 + x)) = 4 ((9 * 10 + x * 10) + x(9 + x)) = 4 ((90 + 10x) + x(9 + x)) = 4 (90 + 10x + (9 * x + x * x)) = 4 (90 + 10x + (9x + x2)) = 4 Combine like terms: 10x + 9x = 19x (90 + 19x + x2) = 4 Solving 90 + 19x + x2 = 4 Solving for variable 'x'. Reorder the terms: 90 + -4 + 19x + x2 = 4 + -4 Combine like terms: 90 + -4 = 86 86 + 19x + x2 = 4 + -4 Combine like terms: 4 + -4 = 0 86 + 19x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-86' to each side of the equation. 86 + 19x + -86 + x2 = 0 + -86 Reorder the terms: 86 + -86 + 19x + x2 = 0 + -86 Combine like terms: 86 + -86 = 0 0 + 19x + x2 = 0 + -86 19x + x2 = 0 + -86 Combine like terms: 0 + -86 = -86 19x + x2 = -86 The x term is 19x. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19x + 90.25 + x2 = -86 + 90.25 Reorder the terms: 90.25 + 19x + x2 = -86 + 90.25 Combine like terms: -86 + 90.25 = 4.25 90.25 + 19x + x2 = 4.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x + 9.5) equal to 2.061552813 and -2.061552813.Subproblem 1
x + 9.5 = 2.061552813 Simplifying x + 9.5 = 2.061552813 Reorder the terms: 9.5 + x = 2.061552813 Solving 9.5 + x = 2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = 2.061552813 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 2.061552813 + -9.5 x = 2.061552813 + -9.5 Combine like terms: 2.061552813 + -9.5 = -7.438447187 x = -7.438447187 Simplifying x = -7.438447187Subproblem 2
x + 9.5 = -2.061552813 Simplifying x + 9.5 = -2.061552813 Reorder the terms: 9.5 + x = -2.061552813 Solving 9.5 + x = -2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = -2.061552813 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -2.061552813 + -9.5 x = -2.061552813 + -9.5 Combine like terms: -2.061552813 + -9.5 = -11.561552813 x = -11.561552813 Simplifying x = -11.561552813Solution
The solution to the problem is based on the solutions from the subproblems. x = {-7.438447187, -11.561552813}
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