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Simplifying (x + -10)(x + -4) = x + 2x + 2 Reorder the terms: (-10 + x)(x + -4) = x + 2x + 2 Reorder the terms: (-10 + x)(-4 + x) = x + 2x + 2 Multiply (-10 + x) * (-4 + x) (-10(-4 + x) + x(-4 + x)) = x + 2x + 2 ((-4 * -10 + x * -10) + x(-4 + x)) = x + 2x + 2 ((40 + -10x) + x(-4 + x)) = x + 2x + 2 (40 + -10x + (-4 * x + x * x)) = x + 2x + 2 (40 + -10x + (-4x + x2)) = x + 2x + 2 Combine like terms: -10x + -4x = -14x (40 + -14x + x2) = x + 2x + 2 Reorder the terms: 40 + -14x + x2 = 2 + x + 2x Combine like terms: x + 2x = 3x 40 + -14x + x2 = 2 + 3x Solving 40 + -14x + x2 = 2 + 3x Solving for variable 'x'. Reorder the terms: 40 + -2 + -14x + -3x + x2 = 2 + 3x + -2 + -3x Combine like terms: 40 + -2 = 38 38 + -14x + -3x + x2 = 2 + 3x + -2 + -3x Combine like terms: -14x + -3x = -17x 38 + -17x + x2 = 2 + 3x + -2 + -3x Reorder the terms: 38 + -17x + x2 = 2 + -2 + 3x + -3x Combine like terms: 2 + -2 = 0 38 + -17x + x2 = 0 + 3x + -3x 38 + -17x + x2 = 3x + -3x Combine like terms: 3x + -3x = 0 38 + -17x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-38' to each side of the equation. 38 + -17x + -38 + x2 = 0 + -38 Reorder the terms: 38 + -38 + -17x + x2 = 0 + -38 Combine like terms: 38 + -38 = 0 0 + -17x + x2 = 0 + -38 -17x + x2 = 0 + -38 Combine like terms: 0 + -38 = -38 -17x + x2 = -38 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = -38 + 72.25 Reorder the terms: 72.25 + -17x + x2 = -38 + 72.25 Combine like terms: -38 + 72.25 = 34.25 72.25 + -17x + x2 = 34.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 34.25 Calculate the square root of the right side: 5.852349955 Break this problem into two subproblems by setting (x + -8.5) equal to 5.852349955 and -5.852349955.Subproblem 1
x + -8.5 = 5.852349955 Simplifying x + -8.5 = 5.852349955 Reorder the terms: -8.5 + x = 5.852349955 Solving -8.5 + x = 5.852349955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 5.852349955 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 5.852349955 + 8.5 x = 5.852349955 + 8.5 Combine like terms: 5.852349955 + 8.5 = 14.352349955 x = 14.352349955 Simplifying x = 14.352349955Subproblem 2
x + -8.5 = -5.852349955 Simplifying x + -8.5 = -5.852349955 Reorder the terms: -8.5 + x = -5.852349955 Solving -8.5 + x = -5.852349955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -5.852349955 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -5.852349955 + 8.5 x = -5.852349955 + 8.5 Combine like terms: -5.852349955 + 8.5 = 2.647650045 x = 2.647650045 Simplifying x = 2.647650045Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.352349955, 2.647650045}
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