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Simplifying (x + -2)(4x + 5) = 9 Reorder the terms: (-2 + x)(4x + 5) = 9 Reorder the terms: (-2 + x)(5 + 4x) = 9 Multiply (-2 + x) * (5 + 4x) (-2(5 + 4x) + x(5 + 4x)) = 9 ((5 * -2 + 4x * -2) + x(5 + 4x)) = 9 ((-10 + -8x) + x(5 + 4x)) = 9 (-10 + -8x + (5 * x + 4x * x)) = 9 (-10 + -8x + (5x + 4x2)) = 9 Combine like terms: -8x + 5x = -3x (-10 + -3x + 4x2) = 9 Solving -10 + -3x + 4x2 = 9 Solving for variable 'x'. Reorder the terms: -10 + -9 + -3x + 4x2 = 9 + -9 Combine like terms: -10 + -9 = -19 -19 + -3x + 4x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -19 + -3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.75 + -0.75x + x2 = 0 Move the constant term to the right: Add '4.75' to each side of the equation. -4.75 + -0.75x + 4.75 + x2 = 0 + 4.75 Reorder the terms: -4.75 + 4.75 + -0.75x + x2 = 0 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + -0.75x + x2 = 0 + 4.75 -0.75x + x2 = 0 + 4.75 Combine like terms: 0 + 4.75 = 4.75 -0.75x + x2 = 4.75 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = 4.75 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 4.75 + 0.140625 Combine like terms: 4.75 + 0.140625 = 4.890625 0.140625 + -0.75x + x2 = 4.890625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 4.890625 Calculate the square root of the right side: 2.211475752 Break this problem into two subproblems by setting (x + -0.375) equal to 2.211475752 and -2.211475752.Subproblem 1
x + -0.375 = 2.211475752 Simplifying x + -0.375 = 2.211475752 Reorder the terms: -0.375 + x = 2.211475752 Solving -0.375 + x = 2.211475752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 2.211475752 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 2.211475752 + 0.375 x = 2.211475752 + 0.375 Combine like terms: 2.211475752 + 0.375 = 2.586475752 x = 2.586475752 Simplifying x = 2.586475752Subproblem 2
x + -0.375 = -2.211475752 Simplifying x + -0.375 = -2.211475752 Reorder the terms: -0.375 + x = -2.211475752 Solving -0.375 + x = -2.211475752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -2.211475752 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -2.211475752 + 0.375 x = -2.211475752 + 0.375 Combine like terms: -2.211475752 + 0.375 = -1.836475752 x = -1.836475752 Simplifying x = -1.836475752Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.586475752, -1.836475752}
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