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Simplifying x(10x + 2) = 9 Reorder the terms: x(2 + 10x) = 9 (2 * x + 10x * x) = 9 (2x + 10x2) = 9 Solving 2x + 10x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + 2x + 10x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 2x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.9 + 0.2x + x2 = 0 Move the constant term to the right: Add '0.9' to each side of the equation. -0.9 + 0.2x + 0.9 + x2 = 0 + 0.9 Reorder the terms: -0.9 + 0.9 + 0.2x + x2 = 0 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + 0.2x + x2 = 0 + 0.9 0.2x + x2 = 0 + 0.9 Combine like terms: 0 + 0.9 = 0.9 0.2x + x2 = 0.9 The x term is 0.2x. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2x + 0.01 + x2 = 0.9 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 0.9 + 0.01 Combine like terms: 0.9 + 0.01 = 0.91 0.01 + 0.2x + x2 = 0.91 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 0.91 Calculate the square root of the right side: 0.953939201 Break this problem into two subproblems by setting (x + 0.1) equal to 0.953939201 and -0.953939201.Subproblem 1
x + 0.1 = 0.953939201 Simplifying x + 0.1 = 0.953939201 Reorder the terms: 0.1 + x = 0.953939201 Solving 0.1 + x = 0.953939201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 0.953939201 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 0.953939201 + -0.1 x = 0.953939201 + -0.1 Combine like terms: 0.953939201 + -0.1 = 0.853939201 x = 0.853939201 Simplifying x = 0.853939201Subproblem 2
x + 0.1 = -0.953939201 Simplifying x + 0.1 = -0.953939201 Reorder the terms: 0.1 + x = -0.953939201 Solving 0.1 + x = -0.953939201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -0.953939201 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -0.953939201 + -0.1 x = -0.953939201 + -0.1 Combine like terms: -0.953939201 + -0.1 = -1.053939201 x = -1.053939201 Simplifying x = -1.053939201Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.853939201, -1.053939201}
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