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Simplifying 4x2 + 8x + 3 = 20x + 310 Reorder the terms: 3 + 8x + 4x2 = 20x + 310 Reorder the terms: 3 + 8x + 4x2 = 310 + 20x Solving 3 + 8x + 4x2 = 310 + 20x Solving for variable 'x'. Reorder the terms: 3 + -310 + 8x + -20x + 4x2 = 310 + 20x + -310 + -20x Combine like terms: 3 + -310 = -307 -307 + 8x + -20x + 4x2 = 310 + 20x + -310 + -20x Combine like terms: 8x + -20x = -12x -307 + -12x + 4x2 = 310 + 20x + -310 + -20x Reorder the terms: -307 + -12x + 4x2 = 310 + -310 + 20x + -20x Combine like terms: 310 + -310 = 0 -307 + -12x + 4x2 = 0 + 20x + -20x -307 + -12x + 4x2 = 20x + -20x Combine like terms: 20x + -20x = 0 -307 + -12x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -76.75 + -3x + x2 = 0 Move the constant term to the right: Add '76.75' to each side of the equation. -76.75 + -3x + 76.75 + x2 = 0 + 76.75 Reorder the terms: -76.75 + 76.75 + -3x + x2 = 0 + 76.75 Combine like terms: -76.75 + 76.75 = 0.00 0.00 + -3x + x2 = 0 + 76.75 -3x + x2 = 0 + 76.75 Combine like terms: 0 + 76.75 = 76.75 -3x + x2 = 76.75 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 76.75 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 76.75 + 2.25 Combine like terms: 76.75 + 2.25 = 79 2.25 + -3x + x2 = 79 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 79 Calculate the square root of the right side: 8.888194417 Break this problem into two subproblems by setting (x + -1.5) equal to 8.888194417 and -8.888194417.Subproblem 1
x + -1.5 = 8.888194417 Simplifying x + -1.5 = 8.888194417 Reorder the terms: -1.5 + x = 8.888194417 Solving -1.5 + x = 8.888194417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 8.888194417 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 8.888194417 + 1.5 x = 8.888194417 + 1.5 Combine like terms: 8.888194417 + 1.5 = 10.388194417 x = 10.388194417 Simplifying x = 10.388194417Subproblem 2
x + -1.5 = -8.888194417 Simplifying x + -1.5 = -8.888194417 Reorder the terms: -1.5 + x = -8.888194417 Solving -1.5 + x = -8.888194417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -8.888194417 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -8.888194417 + 1.5 x = -8.888194417 + 1.5 Combine like terms: -8.888194417 + 1.5 = -7.388194417 x = -7.388194417 Simplifying x = -7.388194417Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.388194417, -7.388194417}
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