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Simplifying 10x2 + 4x + -5 = 0 Reorder the terms: -5 + 4x + 10x2 = 0 Solving -5 + 4x + 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'. -0.5 + 0.4x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 0.4x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 0.4x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 0.4x + x2 = 0 + 0.5 0.4x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 0.4x + x2 = 0.5 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 0.5 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 0.5 + 0.04 Combine like terms: 0.5 + 0.04 = 0.54 0.04 + 0.4x + x2 = 0.54 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 0.54 Calculate the square root of the right side: 0.734846923 Break this problem into two subproblems by setting (x + 0.2) equal to 0.734846923 and -0.734846923.Subproblem 1
x + 0.2 = 0.734846923 Simplifying x + 0.2 = 0.734846923 Reorder the terms: 0.2 + x = 0.734846923 Solving 0.2 + x = 0.734846923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 0.734846923 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 0.734846923 + -0.2 x = 0.734846923 + -0.2 Combine like terms: 0.734846923 + -0.2 = 0.534846923 x = 0.534846923 Simplifying x = 0.534846923Subproblem 2
x + 0.2 = -0.734846923 Simplifying x + 0.2 = -0.734846923 Reorder the terms: 0.2 + x = -0.734846923 Solving 0.2 + x = -0.734846923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -0.734846923 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -0.734846923 + -0.2 x = -0.734846923 + -0.2 Combine like terms: -0.734846923 + -0.2 = -0.934846923 x = -0.934846923 Simplifying x = -0.934846923Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.534846923, -0.934846923}
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