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Simplifying 5x2 + -9x = 1 Reorder the terms: -9x + 5x2 = 1 Solving -9x + 5x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + -9x + 5x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -9x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + -1.8x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -1.8x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -1.8x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -1.8x + x2 = 0 + 0.2 -1.8x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -1.8x + x2 = 0.2 The x term is -1.8x. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8x + 0.81 + x2 = 0.2 + 0.81 Reorder the terms: 0.81 + -1.8x + x2 = 0.2 + 0.81 Combine like terms: 0.2 + 0.81 = 1.01 0.81 + -1.8x + x2 = 1.01 Factor a perfect square on the left side: (x + -0.9)(x + -0.9) = 1.01 Calculate the square root of the right side: 1.004987562 Break this problem into two subproblems by setting (x + -0.9) equal to 1.004987562 and -1.004987562.Subproblem 1
x + -0.9 = 1.004987562 Simplifying x + -0.9 = 1.004987562 Reorder the terms: -0.9 + x = 1.004987562 Solving -0.9 + x = 1.004987562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = 1.004987562 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = 1.004987562 + 0.9 x = 1.004987562 + 0.9 Combine like terms: 1.004987562 + 0.9 = 1.904987562 x = 1.904987562 Simplifying x = 1.904987562Subproblem 2
x + -0.9 = -1.004987562 Simplifying x + -0.9 = -1.004987562 Reorder the terms: -0.9 + x = -1.004987562 Solving -0.9 + x = -1.004987562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = -1.004987562 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = -1.004987562 + 0.9 x = -1.004987562 + 0.9 Combine like terms: -1.004987562 + 0.9 = -0.104987562 x = -0.104987562 Simplifying x = -0.104987562Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.904987562, -0.104987562}
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