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Simplifying 45(x2 + -1) + -9(x + -1) + -2 = 0 Reorder the terms: 45(-1 + x2) + -9(x + -1) + -2 = 0 (-1 * 45 + x2 * 45) + -9(x + -1) + -2 = 0 (-45 + 45x2) + -9(x + -1) + -2 = 0 Reorder the terms: -45 + 45x2 + -9(-1 + x) + -2 = 0 -45 + 45x2 + (-1 * -9 + x * -9) + -2 = 0 -45 + 45x2 + (9 + -9x) + -2 = 0 Reorder the terms: -45 + 9 + -2 + -9x + 45x2 = 0 Combine like terms: -45 + 9 = -36 -36 + -2 + -9x + 45x2 = 0 Combine like terms: -36 + -2 = -38 -38 + -9x + 45x2 = 0 Solving -38 + -9x + 45x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. -0.8444444444 + -0.2x + x2 = 0 Move the constant term to the right: Add '0.8444444444' to each side of the equation. -0.8444444444 + -0.2x + 0.8444444444 + x2 = 0 + 0.8444444444 Reorder the terms: -0.8444444444 + 0.8444444444 + -0.2x + x2 = 0 + 0.8444444444 Combine like terms: -0.8444444444 + 0.8444444444 = 0.0000000000 0.0000000000 + -0.2x + x2 = 0 + 0.8444444444 -0.2x + x2 = 0 + 0.8444444444 Combine like terms: 0 + 0.8444444444 = 0.8444444444 -0.2x + x2 = 0.8444444444 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 = 0.8444444444 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 0.8444444444 + 0.01 Combine like terms: 0.8444444444 + 0.01 = 0.8544444444 0.01 + -0.2x + x2 = 0.8544444444 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 0.8544444444 Calculate the square root of the right side: 0.924361642 Break this problem into two subproblems by setting (x + -0.1) equal to 0.924361642 and -0.924361642.Subproblem 1
x + -0.1 = 0.924361642 Simplifying x + -0.1 = 0.924361642 Reorder the terms: -0.1 + x = 0.924361642 Solving -0.1 + x = 0.924361642 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 = 0.924361642 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 0.924361642 + 0.1 x = 0.924361642 + 0.1 Combine like terms: 0.924361642 + 0.1 = 1.024361642 x = 1.024361642 Simplifying x = 1.024361642Subproblem 2
x + -0.1 = -0.924361642 Simplifying x + -0.1 = -0.924361642 Reorder the terms: -0.1 + x = -0.924361642 Solving -0.1 + x = -0.924361642 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 = -0.924361642 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -0.924361642 + 0.1 x = -0.924361642 + 0.1 Combine like terms: -0.924361642 + 0.1 = -0.824361642 x = -0.824361642 Simplifying x = -0.824361642Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.024361642, -0.824361642}
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