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Simplifying 10x2 + 5x + 1 = 10 Reorder the terms: 1 + 5x + 10x2 = 10 Solving 1 + 5x + 10x2 = 10 Solving for variable 'x'. Reorder the terms: 1 + -10 + 5x + 10x2 = 10 + -10 Combine like terms: 1 + -10 = -9 -9 + 5x + 10x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -9 + 5x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.9 + 0.5x + x2 = 0 Move the constant term to the right: Add '0.9' to each side of the equation. -0.9 + 0.5x + 0.9 + x2 = 0 + 0.9 Reorder the terms: -0.9 + 0.9 + 0.5x + x2 = 0 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + 0.5x + x2 = 0 + 0.9 0.5x + x2 = 0 + 0.9 Combine like terms: 0 + 0.9 = 0.9 0.5x + x2 = 0.9 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 = 0.9 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 0.9 + 0.0625 Combine like terms: 0.9 + 0.0625 = 0.9625 0.0625 + 0.5x + x2 = 0.9625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 0.9625 Calculate the square root of the right side: 0.981070844 Break this problem into two subproblems by setting (x + 0.25) equal to 0.981070844 and -0.981070844.Subproblem 1
x + 0.25 = 0.981070844 Simplifying x + 0.25 = 0.981070844 Reorder the terms: 0.25 + x = 0.981070844 Solving 0.25 + x = 0.981070844 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 = 0.981070844 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 0.981070844 + -0.25 x = 0.981070844 + -0.25 Combine like terms: 0.981070844 + -0.25 = 0.731070844 x = 0.731070844 Simplifying x = 0.731070844Subproblem 2
x + 0.25 = -0.981070844 Simplifying x + 0.25 = -0.981070844 Reorder the terms: 0.25 + x = -0.981070844 Solving 0.25 + x = -0.981070844 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 = -0.981070844 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -0.981070844 + -0.25 x = -0.981070844 + -0.25 Combine like terms: -0.981070844 + -0.25 = -1.231070844 x = -1.231070844 Simplifying x = -1.231070844Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.731070844, -1.231070844}
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