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Simplifying 10(x2 + -1x + -6) = 1 Reorder the terms: 10(-6 + -1x + x2) = 1 (-6 * 10 + -1x * 10 + x2 * 10) = 1 (-60 + -10x + 10x2) = 1 Solving -60 + -10x + 10x2 = 1 Solving for variable 'x'. Reorder the terms: -60 + -1 + -10x + 10x2 = 1 + -1 Combine like terms: -60 + -1 = -61 -61 + -10x + 10x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -61 + -10x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -6.1 + -1x + x2 = 0 Move the constant term to the right: Add '6.1' to each side of the equation. -6.1 + -1x + 6.1 + x2 = 0 + 6.1 Reorder the terms: -6.1 + 6.1 + -1x + x2 = 0 + 6.1 Combine like terms: -6.1 + 6.1 = 0.0 0.0 + -1x + x2 = 0 + 6.1 -1x + x2 = 0 + 6.1 Combine like terms: 0 + 6.1 = 6.1 -1x + x2 = 6.1 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 6.1 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 6.1 + 0.25 Combine like terms: 6.1 + 0.25 = 6.35 0.25 + -1x + x2 = 6.35 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 6.35 Calculate the square root of the right side: 2.519920634 Break this problem into two subproblems by setting (x + -0.5) equal to 2.519920634 and -2.519920634.Subproblem 1
x + -0.5 = 2.519920634 Simplifying x + -0.5 = 2.519920634 Reorder the terms: -0.5 + x = 2.519920634 Solving -0.5 + x = 2.519920634 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 2.519920634 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 2.519920634 + 0.5 x = 2.519920634 + 0.5 Combine like terms: 2.519920634 + 0.5 = 3.019920634 x = 3.019920634 Simplifying x = 3.019920634Subproblem 2
x + -0.5 = -2.519920634 Simplifying x + -0.5 = -2.519920634 Reorder the terms: -0.5 + x = -2.519920634 Solving -0.5 + x = -2.519920634 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -2.519920634 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -2.519920634 + 0.5 x = -2.519920634 + 0.5 Combine like terms: -2.519920634 + 0.5 = -2.019920634 x = -2.019920634 Simplifying x = -2.019920634Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.019920634, -2.019920634}
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