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Simplifying (x + 10)(x + 4) = 3 Reorder the terms: (10 + x)(x + 4) = 3 Reorder the terms: (10 + x)(4 + x) = 3 Multiply (10 + x) * (4 + x) (10(4 + x) + x(4 + x)) = 3 ((4 * 10 + x * 10) + x(4 + x)) = 3 ((40 + 10x) + x(4 + x)) = 3 (40 + 10x + (4 * x + x * x)) = 3 (40 + 10x + (4x + x2)) = 3 Combine like terms: 10x + 4x = 14x (40 + 14x + x2) = 3 Solving 40 + 14x + x2 = 3 Solving for variable 'x'. Reorder the terms: 40 + -3 + 14x + x2 = 3 + -3 Combine like terms: 40 + -3 = 37 37 + 14x + x2 = 3 + -3 Combine like terms: 3 + -3 = 0 37 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-37' to each side of the equation. 37 + 14x + -37 + x2 = 0 + -37 Reorder the terms: 37 + -37 + 14x + x2 = 0 + -37 Combine like terms: 37 + -37 = 0 0 + 14x + x2 = 0 + -37 14x + x2 = 0 + -37 Combine like terms: 0 + -37 = -37 14x + x2 = -37 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = -37 + 49 Reorder the terms: 49 + 14x + x2 = -37 + 49 Combine like terms: -37 + 49 = 12 49 + 14x + x2 = 12 Factor a perfect square on the left side: (x + 7)(x + 7) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x + 7) equal to 3.464101615 and -3.464101615.Subproblem 1
x + 7 = 3.464101615 Simplifying x + 7 = 3.464101615 Reorder the terms: 7 + x = 3.464101615 Solving 7 + x = 3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 3.464101615 + -7 Combine like terms: 7 + -7 = 0 0 + x = 3.464101615 + -7 x = 3.464101615 + -7 Combine like terms: 3.464101615 + -7 = -3.535898385 x = -3.535898385 Simplifying x = -3.535898385Subproblem 2
x + 7 = -3.464101615 Simplifying x + 7 = -3.464101615 Reorder the terms: 7 + x = -3.464101615 Solving 7 + x = -3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -3.464101615 + -7 Combine like terms: 7 + -7 = 0 0 + x = -3.464101615 + -7 x = -3.464101615 + -7 Combine like terms: -3.464101615 + -7 = -10.464101615 x = -10.464101615 Simplifying x = -10.464101615Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.535898385, -10.464101615}
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