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Simplifying 4x2 + 3x + 5 = 24 Reorder the terms: 5 + 3x + 4x2 = 24 Solving 5 + 3x + 4x2 = 24 Solving for variable 'x'. Reorder the terms: 5 + -24 + 3x + 4x2 = 24 + -24 Combine like terms: 5 + -24 = -19 -19 + 3x + 4x2 = 24 + -24 Combine like terms: 24 + -24 = 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 = 1.836475752 x = 1.836475752 Simplifying x = 1.836475752Subproblem 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 = -2.586475752 x = -2.586475752 Simplifying x = -2.586475752Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.836475752, -2.586475752}
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