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Simplifying 2x2 + 8x + 3 = 10 Reorder the terms: 3 + 8x + 2x2 = 10 Solving 3 + 8x + 2x2 = 10 Solving for variable 'x'. Reorder the terms: 3 + -10 + 8x + 2x2 = 10 + -10 Combine like terms: 3 + -10 = -7 -7 + 8x + 2x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -7 + 8x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + 4x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 4x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 4x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 4x + x2 = 0 + 3.5 4x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 4x + x2 = 3.5 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 3.5 + 4 Reorder the terms: 4 + 4x + x2 = 3.5 + 4 Combine like terms: 3.5 + 4 = 7.5 4 + 4x + x2 = 7.5 Factor a perfect square on the left side: (x + 2)(x + 2) = 7.5 Calculate the square root of the right side: 2.738612788 Break this problem into two subproblems by setting (x + 2) equal to 2.738612788 and -2.738612788.Subproblem 1
x + 2 = 2.738612788 Simplifying x + 2 = 2.738612788 Reorder the terms: 2 + x = 2.738612788 Solving 2 + x = 2.738612788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 2.738612788 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.738612788 + -2 x = 2.738612788 + -2 Combine like terms: 2.738612788 + -2 = 0.738612788 x = 0.738612788 Simplifying x = 0.738612788Subproblem 2
x + 2 = -2.738612788 Simplifying x + 2 = -2.738612788 Reorder the terms: 2 + x = -2.738612788 Solving 2 + x = -2.738612788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -2.738612788 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.738612788 + -2 x = -2.738612788 + -2 Combine like terms: -2.738612788 + -2 = -4.738612788 x = -4.738612788 Simplifying x = -4.738612788Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.738612788, -4.738612788}
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