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Simplifying 10x2 + 11x + 1 = 5 Reorder the terms: 1 + 11x + 10x2 = 5 Solving 1 + 11x + 10x2 = 5 Solving for variable 'x'. Reorder the terms: 1 + -5 + 11x + 10x2 = 5 + -5 Combine like terms: 1 + -5 = -4 -4 + 11x + 10x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -4 + 11x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.4 + 1.1x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 1.1x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 1.1x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 1.1x + x2 = 0 + 0.4 1.1x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 1.1x + x2 = 0.4 The x term is 1.1x. Take half its coefficient (0.55). Square it (0.3025) and add it to both sides. Add '0.3025' to each side of the equation. 1.1x + 0.3025 + x2 = 0.4 + 0.3025 Reorder the terms: 0.3025 + 1.1x + x2 = 0.4 + 0.3025 Combine like terms: 0.4 + 0.3025 = 0.7025 0.3025 + 1.1x + x2 = 0.7025 Factor a perfect square on the left side: (x + 0.55)(x + 0.55) = 0.7025 Calculate the square root of the right side: 0.838152731 Break this problem into two subproblems by setting (x + 0.55) equal to 0.838152731 and -0.838152731.Subproblem 1
x + 0.55 = 0.838152731 Simplifying x + 0.55 = 0.838152731 Reorder the terms: 0.55 + x = 0.838152731 Solving 0.55 + x = 0.838152731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.55' to each side of the equation. 0.55 + -0.55 + x = 0.838152731 + -0.55 Combine like terms: 0.55 + -0.55 = 0.00 0.00 + x = 0.838152731 + -0.55 x = 0.838152731 + -0.55 Combine like terms: 0.838152731 + -0.55 = 0.288152731 x = 0.288152731 Simplifying x = 0.288152731Subproblem 2
x + 0.55 = -0.838152731 Simplifying x + 0.55 = -0.838152731 Reorder the terms: 0.55 + x = -0.838152731 Solving 0.55 + x = -0.838152731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.55' to each side of the equation. 0.55 + -0.55 + x = -0.838152731 + -0.55 Combine like terms: 0.55 + -0.55 = 0.00 0.00 + x = -0.838152731 + -0.55 x = -0.838152731 + -0.55 Combine like terms: -0.838152731 + -0.55 = -1.388152731 x = -1.388152731 Simplifying x = -1.388152731Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.288152731, -1.388152731}
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