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Simplifying x2 + -8x + 40 = 5x + 32 Reorder the terms: 40 + -8x + x2 = 5x + 32 Reorder the terms: 40 + -8x + x2 = 32 + 5x Solving 40 + -8x + x2 = 32 + 5x Solving for variable 'x'. Reorder the terms: 40 + -32 + -8x + -5x + x2 = 32 + 5x + -32 + -5x Combine like terms: 40 + -32 = 8 8 + -8x + -5x + x2 = 32 + 5x + -32 + -5x Combine like terms: -8x + -5x = -13x 8 + -13x + x2 = 32 + 5x + -32 + -5x Reorder the terms: 8 + -13x + x2 = 32 + -32 + 5x + -5x Combine like terms: 32 + -32 = 0 8 + -13x + x2 = 0 + 5x + -5x 8 + -13x + x2 = 5x + -5x Combine like terms: 5x + -5x = 0 8 + -13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -13x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -13x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -13x + x2 = 0 + -8 -13x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -13x + x2 = -8 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = -8 + 42.25 Reorder the terms: 42.25 + -13x + x2 = -8 + 42.25 Combine like terms: -8 + 42.25 = 34.25 42.25 + -13x + x2 = 34.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 34.25 Calculate the square root of the right side: 5.852349955 Break this problem into two subproblems by setting (x + -6.5) equal to 5.852349955 and -5.852349955.Subproblem 1
x + -6.5 = 5.852349955 Simplifying x + -6.5 = 5.852349955 Reorder the terms: -6.5 + x = 5.852349955 Solving -6.5 + x = 5.852349955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 5.852349955 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 5.852349955 + 6.5 x = 5.852349955 + 6.5 Combine like terms: 5.852349955 + 6.5 = 12.352349955 x = 12.352349955 Simplifying x = 12.352349955Subproblem 2
x + -6.5 = -5.852349955 Simplifying x + -6.5 = -5.852349955 Reorder the terms: -6.5 + x = -5.852349955 Solving -6.5 + x = -5.852349955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -5.852349955 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -5.852349955 + 6.5 x = -5.852349955 + 6.5 Combine like terms: -5.852349955 + 6.5 = 0.647650045 x = 0.647650045 Simplifying x = 0.647650045Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.352349955, 0.647650045}
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