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Simplifying 10x2 + 5x + (-8) = 0 10x2 + 5x + -8 = 0 Reorder the terms: -8 + 5x + 10x2 = 0 Solving -8 + 5x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.8 + 0.5x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 0.5x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + 0.5x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 0.5x + x2 = 0 + 0.8 0.5x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 0.5x + x2 = 0.8 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 0.8 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 0.8 + 0.0625 Combine like terms: 0.8 + 0.0625 = 0.8625 0.0625 + 0.5x + x2 = 0.8625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 0.8625 Calculate the square root of the right side: 0.928708781 Break this problem into two subproblems by setting (x + 0.25) equal to 0.928708781 and -0.928708781.Subproblem 1
x + 0.25 = 0.928708781 Simplifying x + 0.25 = 0.928708781 Reorder the terms: 0.25 + x = 0.928708781 Solving 0.25 + x = 0.928708781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 0.928708781 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 0.928708781 + -0.25 x = 0.928708781 + -0.25 Combine like terms: 0.928708781 + -0.25 = 0.678708781 x = 0.678708781 Simplifying x = 0.678708781Subproblem 2
x + 0.25 = -0.928708781 Simplifying x + 0.25 = -0.928708781 Reorder the terms: 0.25 + x = -0.928708781 Solving 0.25 + x = -0.928708781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -0.928708781 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -0.928708781 + -0.25 x = -0.928708781 + -0.25 Combine like terms: -0.928708781 + -0.25 = -1.178708781 x = -1.178708781 Simplifying x = -1.178708781Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.678708781, -1.178708781}
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