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Simplifying 10x2 + -8x + -5 = 0 Reorder the terms: -5 + -8x + 10x2 = 0 Solving -5 + -8x + 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 + -0.8x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.8x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.8x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.8x + x2 = 0 + 0.5 -0.8x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -0.8x + x2 = 0.5 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = 0.5 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 0.5 + 0.16 Combine like terms: 0.5 + 0.16 = 0.66 0.16 + -0.8x + x2 = 0.66 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 0.66 Calculate the square root of the right side: 0.81240384 Break this problem into two subproblems by setting (x + -0.4) equal to 0.81240384 and -0.81240384.Subproblem 1
x + -0.4 = 0.81240384 Simplifying x + -0.4 = 0.81240384 Reorder the terms: -0.4 + x = 0.81240384 Solving -0.4 + x = 0.81240384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 0.81240384 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 0.81240384 + 0.4 x = 0.81240384 + 0.4 Combine like terms: 0.81240384 + 0.4 = 1.21240384 x = 1.21240384 Simplifying x = 1.21240384Subproblem 2
x + -0.4 = -0.81240384 Simplifying x + -0.4 = -0.81240384 Reorder the terms: -0.4 + x = -0.81240384 Solving -0.4 + x = -0.81240384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -0.81240384 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -0.81240384 + 0.4 x = -0.81240384 + 0.4 Combine like terms: -0.81240384 + 0.4 = -0.41240384 x = -0.41240384 Simplifying x = -0.41240384Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.21240384, -0.41240384}
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