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Simplifying 30x2 + -10 = 5x + -1 Reorder the terms: -10 + 30x2 = 5x + -1 Reorder the terms: -10 + 30x2 = -1 + 5x Solving -10 + 30x2 = -1 + 5x Solving for variable 'x'. Reorder the terms: -10 + 1 + -5x + 30x2 = -1 + 5x + 1 + -5x Combine like terms: -10 + 1 = -9 -9 + -5x + 30x2 = -1 + 5x + 1 + -5x Reorder the terms: -9 + -5x + 30x2 = -1 + 1 + 5x + -5x Combine like terms: -1 + 1 = 0 -9 + -5x + 30x2 = 0 + 5x + -5x -9 + -5x + 30x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -9 + -5x + 30x2 = 0 Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. -0.3 + -0.1666666667x + x2 = 0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + -0.1666666667x + 0.3 + x2 = 0 + 0.3 Reorder the terms: -0.3 + 0.3 + -0.1666666667x + x2 = 0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + -0.1666666667x + x2 = 0 + 0.3 -0.1666666667x + x2 = 0 + 0.3 Combine like terms: 0 + 0.3 = 0.3 -0.1666666667x + x2 = 0.3 The x term is -0.1666666667x. Take half its coefficient (-0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. -0.1666666667x + 0.006944444447 + x2 = 0.3 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667x + x2 = 0.3 + 0.006944444447 Combine like terms: 0.3 + 0.006944444447 = 0.306944444447 0.006944444447 + -0.1666666667x + x2 = 0.306944444447 Factor a perfect square on the left side: (x + -0.08333333335)(x + -0.08333333335) = 0.306944444447 Calculate the square root of the right side: 0.554025671 Break this problem into two subproblems by setting (x + -0.08333333335) equal to 0.554025671 and -0.554025671.Subproblem 1
x + -0.08333333335 = 0.554025671 Simplifying x + -0.08333333335 = 0.554025671 Reorder the terms: -0.08333333335 + x = 0.554025671 Solving -0.08333333335 + x = 0.554025671 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = 0.554025671 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = 0.554025671 + 0.08333333335 x = 0.554025671 + 0.08333333335 Combine like terms: 0.554025671 + 0.08333333335 = 0.63735900435 x = 0.63735900435 Simplifying x = 0.63735900435Subproblem 2
x + -0.08333333335 = -0.554025671 Simplifying x + -0.08333333335 = -0.554025671 Reorder the terms: -0.08333333335 + x = -0.554025671 Solving -0.08333333335 + x = -0.554025671 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = -0.554025671 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = -0.554025671 + 0.08333333335 x = -0.554025671 + 0.08333333335 Combine like terms: -0.554025671 + 0.08333333335 = -0.47069233765 x = -0.47069233765 Simplifying x = -0.47069233765Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.63735900435, -0.47069233765}
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