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Simplifying 10x2 + 23x + 10 = 0 Reorder the terms: 10 + 23x + 10x2 = 0 Solving 10 + 23x + 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'. 1 + 2.3x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 2.3x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 2.3x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2.3x + x2 = 0 + -1 2.3x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 2.3x + x2 = -1 The x term is 2.3x. Take half its coefficient (1.15). Square it (1.3225) and add it to both sides. Add '1.3225' to each side of the equation. 2.3x + 1.3225 + x2 = -1 + 1.3225 Reorder the terms: 1.3225 + 2.3x + x2 = -1 + 1.3225 Combine like terms: -1 + 1.3225 = 0.3225 1.3225 + 2.3x + x2 = 0.3225 Factor a perfect square on the left side: (x + 1.15)(x + 1.15) = 0.3225 Calculate the square root of the right side: 0.567890835 Break this problem into two subproblems by setting (x + 1.15) equal to 0.567890835 and -0.567890835.Subproblem 1
x + 1.15 = 0.567890835 Simplifying x + 1.15 = 0.567890835 Reorder the terms: 1.15 + x = 0.567890835 Solving 1.15 + x = 0.567890835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.15' to each side of the equation. 1.15 + -1.15 + x = 0.567890835 + -1.15 Combine like terms: 1.15 + -1.15 = 0.00 0.00 + x = 0.567890835 + -1.15 x = 0.567890835 + -1.15 Combine like terms: 0.567890835 + -1.15 = -0.582109165 x = -0.582109165 Simplifying x = -0.582109165Subproblem 2
x + 1.15 = -0.567890835 Simplifying x + 1.15 = -0.567890835 Reorder the terms: 1.15 + x = -0.567890835 Solving 1.15 + x = -0.567890835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.15' to each side of the equation. 1.15 + -1.15 + x = -0.567890835 + -1.15 Combine like terms: 1.15 + -1.15 = 0.00 0.00 + x = -0.567890835 + -1.15 x = -0.567890835 + -1.15 Combine like terms: -0.567890835 + -1.15 = -1.717890835 x = -1.717890835 Simplifying x = -1.717890835Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.582109165, -1.717890835}
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