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Simplifying 4x + 5 = 2x2 + -8 Reorder the terms: 5 + 4x = 2x2 + -8 Reorder the terms: 5 + 4x = -8 + 2x2 Solving 5 + 4x = -8 + 2x2 Solving for variable 'x'. Reorder the terms: 5 + 8 + 4x + -2x2 = -8 + 2x2 + 8 + -2x2 Combine like terms: 5 + 8 = 13 13 + 4x + -2x2 = -8 + 2x2 + 8 + -2x2 Reorder the terms: 13 + 4x + -2x2 = -8 + 8 + 2x2 + -2x2 Combine like terms: -8 + 8 = 0 13 + 4x + -2x2 = 0 + 2x2 + -2x2 13 + 4x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 13 + 4x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -6.5 + -2x + x2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + -2x + 6.5 + x2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + -2x + x2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + -2x + x2 = 0 + 6.5 -2x + x2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 -2x + x2 = 6.5 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 6.5 + 1 Reorder the terms: 1 + -2x + x2 = 6.5 + 1 Combine like terms: 6.5 + 1 = 7.5 1 + -2x + x2 = 7.5 Factor a perfect square on the left side: (x + -1)(x + -1) = 7.5 Calculate the square root of the right side: 2.738612788 Break this problem into two subproblems by setting (x + -1) equal to 2.738612788 and -2.738612788.Subproblem 1
x + -1 = 2.738612788 Simplifying x + -1 = 2.738612788 Reorder the terms: -1 + x = 2.738612788 Solving -1 + x = 2.738612788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.738612788 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.738612788 + 1 x = 2.738612788 + 1 Combine like terms: 2.738612788 + 1 = 3.738612788 x = 3.738612788 Simplifying x = 3.738612788Subproblem 2
x + -1 = -2.738612788 Simplifying x + -1 = -2.738612788 Reorder the terms: -1 + x = -2.738612788 Solving -1 + x = -2.738612788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.738612788 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.738612788 + 1 x = -2.738612788 + 1 Combine like terms: -2.738612788 + 1 = -1.738612788 x = -1.738612788 Simplifying x = -1.738612788Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.738612788, -1.738612788}
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