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Simplifying (x + 5)(x + -4) = 14 Reorder the terms: (5 + x)(x + -4) = 14 Reorder the terms: (5 + x)(-4 + x) = 14 Multiply (5 + x) * (-4 + x) (5(-4 + x) + x(-4 + x)) = 14 ((-4 * 5 + x * 5) + x(-4 + x)) = 14 ((-20 + 5x) + x(-4 + x)) = 14 (-20 + 5x + (-4 * x + x * x)) = 14 (-20 + 5x + (-4x + x2)) = 14 Combine like terms: 5x + -4x = 1x (-20 + 1x + x2) = 14 Solving -20 + 1x + x2 = 14 Solving for variable 'x'. Reorder the terms: -20 + -14 + 1x + x2 = 14 + -14 Combine like terms: -20 + -14 = -34 -34 + 1x + x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -34 + 1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '34' to each side of the equation. -34 + 1x + 34 + x2 = 0 + 34 Reorder the terms: -34 + 34 + 1x + x2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + 1x + x2 = 0 + 34 1x + x2 = 0 + 34 Combine like terms: 0 + 34 = 34 1x + x2 = 34 The x term is 1x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 34 + 0.25 Reorder the terms: 0.25 + x + x2 = 34 + 0.25 Combine like terms: 34 + 0.25 = 34.25 0.25 + x + x2 = 34.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 34.25 Calculate the square root of the right side: 5.852349955 Break this problem into two subproblems by setting (x + 0.5) equal to 5.852349955 and -5.852349955.Subproblem 1
x + 0.5 = 5.852349955 Simplifying x + 0.5 = 5.852349955 Reorder the terms: 0.5 + x = 5.852349955 Solving 0.5 + x = 5.852349955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 5.852349955 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.852349955 + -0.5 x = 5.852349955 + -0.5 Combine like terms: 5.852349955 + -0.5 = 5.352349955 x = 5.352349955 Simplifying x = 5.352349955Subproblem 2
x + 0.5 = -5.852349955 Simplifying x + 0.5 = -5.852349955 Reorder the terms: 0.5 + x = -5.852349955 Solving 0.5 + x = -5.852349955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -5.852349955 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.852349955 + -0.5 x = -5.852349955 + -0.5 Combine like terms: -5.852349955 + -0.5 = -6.352349955 x = -6.352349955 Simplifying x = -6.352349955Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.352349955, -6.352349955}
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