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Simplifying 5x2 = x + 1 Reorder the terms: 5x2 = 1 + x Solving 5x2 = 1 + x Solving for variable 'x'. Reorder the terms: -1 + -1x + 5x2 = 1 + x + -1 + -1x Reorder the terms: -1 + -1x + 5x2 = 1 + -1 + x + -1x Combine like terms: 1 + -1 = 0 -1 + -1x + 5x2 = 0 + x + -1x -1 + -1x + 5x2 = x + -1x Combine like terms: x + -1x = 0 -1 + -1x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + -0.2x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -0.2x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -0.2x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -0.2x + x2 = 0 + 0.2 -0.2x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -0.2x + x2 = 0.2 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 = 0.2 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 0.2 + 0.01 Combine like terms: 0.2 + 0.01 = 0.21 0.01 + -0.2x + x2 = 0.21 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 0.21 Calculate the square root of the right side: 0.458257569 Break this problem into two subproblems by setting (x + -0.1) equal to 0.458257569 and -0.458257569.Subproblem 1
x + -0.1 = 0.458257569 Simplifying x + -0.1 = 0.458257569 Reorder the terms: -0.1 + x = 0.458257569 Solving -0.1 + x = 0.458257569 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 = 0.458257569 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 0.458257569 + 0.1 x = 0.458257569 + 0.1 Combine like terms: 0.458257569 + 0.1 = 0.558257569 x = 0.558257569 Simplifying x = 0.558257569Subproblem 2
x + -0.1 = -0.458257569 Simplifying x + -0.1 = -0.458257569 Reorder the terms: -0.1 + x = -0.458257569 Solving -0.1 + x = -0.458257569 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 = -0.458257569 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -0.458257569 + 0.1 x = -0.458257569 + 0.1 Combine like terms: -0.458257569 + 0.1 = -0.358257569 x = -0.358257569 Simplifying x = -0.358257569Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.558257569, -0.358257569}
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