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Simplifying 2x * 2x + 5x + -8 = 0 Reorder the terms for easier multiplication: 2 * 2x * x + 5x + -8 = 0 Multiply 2 * 2 4x * x + 5x + -8 = 0 Multiply x * x 4x2 + 5x + -8 = 0 Reorder the terms: -8 + 5x + 4x2 = 0 Solving -8 + 5x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2 + 1.25x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 1.25x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 1.25x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 1.25x + x2 = 0 + 2 1.25x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 1.25x + x2 = 2 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = 2 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 2 + 0.390625 Combine like terms: 2 + 0.390625 = 2.390625 0.390625 + 1.25x + x2 = 2.390625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 2.390625 Calculate the square root of the right side: 1.54616461 Break this problem into two subproblems by setting (x + 0.625) equal to 1.54616461 and -1.54616461.Subproblem 1
x + 0.625 = 1.54616461 Simplifying x + 0.625 = 1.54616461 Reorder the terms: 0.625 + x = 1.54616461 Solving 0.625 + x = 1.54616461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 1.54616461 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 1.54616461 + -0.625 x = 1.54616461 + -0.625 Combine like terms: 1.54616461 + -0.625 = 0.92116461 x = 0.92116461 Simplifying x = 0.92116461Subproblem 2
x + 0.625 = -1.54616461 Simplifying x + 0.625 = -1.54616461 Reorder the terms: 0.625 + x = -1.54616461 Solving 0.625 + x = -1.54616461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -1.54616461 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -1.54616461 + -0.625 x = -1.54616461 + -0.625 Combine like terms: -1.54616461 + -0.625 = -2.17116461 x = -2.17116461 Simplifying x = -2.17116461Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.92116461, -2.17116461}
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