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Simplifying 6x2 + 0.1x = 0.09 Reorder the terms: 0.1x + 6x2 = 0.09 Solving 0.1x + 6x2 = 0.09 Solving for variable 'x'. Reorder the terms: -0.09 + 0.1x + 6x2 = 0.09 + -0.09 Combine like terms: 0.09 + -0.09 = 0.00 -0.09 + 0.1x + 6x2 = 0.00 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.015 + 0.01666666667x + x2 = 0.00 Move the constant term to the right: Add '0.015' to each side of the equation. -0.015 + 0.01666666667x + 0.015 + x2 = 0.00 + 0.015 Reorder the terms: -0.015 + 0.015 + 0.01666666667x + x2 = 0.00 + 0.015 Combine like terms: -0.015 + 0.015 = 0.000 0.000 + 0.01666666667x + x2 = 0.00 + 0.015 0.01666666667x + x2 = 0.00 + 0.015 Combine like terms: 0.00 + 0.015 = 0.015 0.01666666667x + x2 = 0.015 The x term is 0.01666666667x. Take half its coefficient (0.008333333335). Square it (0.00006944444447) and add it to both sides. Add '0.00006944444447' to each side of the equation. 0.01666666667x + 0.00006944444447 + x2 = 0.015 + 0.00006944444447 Reorder the terms: 0.00006944444447 + 0.01666666667x + x2 = 0.015 + 0.00006944444447 Combine like terms: 0.015 + 0.00006944444447 = 0.01506944444447 0.00006944444447 + 0.01666666667x + x2 = 0.01506944444447 Factor a perfect square on the left side: (x + 0.008333333335)(x + 0.008333333335) = 0.01506944444447 Calculate the square root of the right side: 0.122757666 Break this problem into two subproblems by setting (x + 0.008333333335) equal to 0.122757666 and -0.122757666.Subproblem 1
x + 0.008333333335 = 0.122757666 Simplifying x + 0.008333333335 = 0.122757666 Reorder the terms: 0.008333333335 + x = 0.122757666 Solving 0.008333333335 + x = 0.122757666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.008333333335' to each side of the equation. 0.008333333335 + -0.008333333335 + x = 0.122757666 + -0.008333333335 Combine like terms: 0.008333333335 + -0.008333333335 = 0.000000000000 0.000000000000 + x = 0.122757666 + -0.008333333335 x = 0.122757666 + -0.008333333335 Combine like terms: 0.122757666 + -0.008333333335 = 0.114424332665 x = 0.114424332665 Simplifying x = 0.114424332665Subproblem 2
x + 0.008333333335 = -0.122757666 Simplifying x + 0.008333333335 = -0.122757666 Reorder the terms: 0.008333333335 + x = -0.122757666 Solving 0.008333333335 + x = -0.122757666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.008333333335' to each side of the equation. 0.008333333335 + -0.008333333335 + x = -0.122757666 + -0.008333333335 Combine like terms: 0.008333333335 + -0.008333333335 = 0.000000000000 0.000000000000 + x = -0.122757666 + -0.008333333335 x = -0.122757666 + -0.008333333335 Combine like terms: -0.122757666 + -0.008333333335 = -0.131090999335 x = -0.131090999335 Simplifying x = -0.131090999335Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.114424332665, -0.131090999335}
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