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Simplifying 10x2 + 17x + 4 = 0 Reorder the terms: 4 + 17x + 10x2 = 0 Solving 4 + 17x + 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'. 0.4 + 1.7x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + 1.7x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + 1.7x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 1.7x + x2 = 0 + -0.4 1.7x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 1.7x + x2 = -0.4 The x term is 1.7x. Take half its coefficient (0.85). Square it (0.7225) and add it to both sides. Add '0.7225' to each side of the equation. 1.7x + 0.7225 + x2 = -0.4 + 0.7225 Reorder the terms: 0.7225 + 1.7x + x2 = -0.4 + 0.7225 Combine like terms: -0.4 + 0.7225 = 0.3225 0.7225 + 1.7x + x2 = 0.3225 Factor a perfect square on the left side: (x + 0.85)(x + 0.85) = 0.3225 Calculate the square root of the right side: 0.567890835 Break this problem into two subproblems by setting (x + 0.85) equal to 0.567890835 and -0.567890835.Subproblem 1
x + 0.85 = 0.567890835 Simplifying x + 0.85 = 0.567890835 Reorder the terms: 0.85 + x = 0.567890835 Solving 0.85 + x = 0.567890835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.85' to each side of the equation. 0.85 + -0.85 + x = 0.567890835 + -0.85 Combine like terms: 0.85 + -0.85 = 0.00 0.00 + x = 0.567890835 + -0.85 x = 0.567890835 + -0.85 Combine like terms: 0.567890835 + -0.85 = -0.282109165 x = -0.282109165 Simplifying x = -0.282109165Subproblem 2
x + 0.85 = -0.567890835 Simplifying x + 0.85 = -0.567890835 Reorder the terms: 0.85 + x = -0.567890835 Solving 0.85 + x = -0.567890835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.85' to each side of the equation. 0.85 + -0.85 + x = -0.567890835 + -0.85 Combine like terms: 0.85 + -0.85 = 0.00 0.00 + x = -0.567890835 + -0.85 x = -0.567890835 + -0.85 Combine like terms: -0.567890835 + -0.85 = -1.417890835 x = -1.417890835 Simplifying x = -1.417890835Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.282109165, -1.417890835}
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