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Simplifying 150x2 = 0.3 + x Solving 150x2 = 0.3 + x Solving for variable 'x'. Reorder the terms: -0.3 + -1x + 150x2 = 0.3 + x + -0.3 + -1x Reorder the terms: -0.3 + -1x + 150x2 = 0.3 + -0.3 + x + -1x Combine like terms: 0.3 + -0.3 = 0.0 -0.3 + -1x + 150x2 = 0.0 + x + -1x -0.3 + -1x + 150x2 = x + -1x Combine like terms: x + -1x = 0 -0.3 + -1x + 150x2 = 0 Begin completing the square. Divide all terms by 150 the coefficient of the squared term: Divide each side by '150'. -0.002 + -0.006666666667x + x2 = 0 Move the constant term to the right: Add '0.002' to each side of the equation. -0.002 + -0.006666666667x + 0.002 + x2 = 0 + 0.002 Reorder the terms: -0.002 + 0.002 + -0.006666666667x + x2 = 0 + 0.002 Combine like terms: -0.002 + 0.002 = 0.000 0.000 + -0.006666666667x + x2 = 0 + 0.002 -0.006666666667x + x2 = 0 + 0.002 Combine like terms: 0 + 0.002 = 0.002 -0.006666666667x + x2 = 0.002 The x term is -0.006666666667x. Take half its coefficient (-0.003333333334). Square it (0.00001111111112) and add it to both sides. Add '0.00001111111112' to each side of the equation. -0.006666666667x + 0.00001111111112 + x2 = 0.002 + 0.00001111111112 Reorder the terms: 0.00001111111112 + -0.006666666667x + x2 = 0.002 + 0.00001111111112 Combine like terms: 0.002 + 0.00001111111112 = 0.00201111111112 0.00001111111112 + -0.006666666667x + x2 = 0.00201111111112 Factor a perfect square on the left side: (x + -0.003333333334)(x + -0.003333333334) = 0.00201111111112 Calculate the square root of the right side: 0.044845413 Break this problem into two subproblems by setting (x + -0.003333333334) equal to 0.044845413 and -0.044845413.Subproblem 1
x + -0.003333333334 = 0.044845413 Simplifying x + -0.003333333334 = 0.044845413 Reorder the terms: -0.003333333334 + x = 0.044845413 Solving -0.003333333334 + x = 0.044845413 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.003333333334' to each side of the equation. -0.003333333334 + 0.003333333334 + x = 0.044845413 + 0.003333333334 Combine like terms: -0.003333333334 + 0.003333333334 = 0.000000000000 0.000000000000 + x = 0.044845413 + 0.003333333334 x = 0.044845413 + 0.003333333334 Combine like terms: 0.044845413 + 0.003333333334 = 0.048178746334 x = 0.048178746334 Simplifying x = 0.048178746334Subproblem 2
x + -0.003333333334 = -0.044845413 Simplifying x + -0.003333333334 = -0.044845413 Reorder the terms: -0.003333333334 + x = -0.044845413 Solving -0.003333333334 + x = -0.044845413 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.003333333334' to each side of the equation. -0.003333333334 + 0.003333333334 + x = -0.044845413 + 0.003333333334 Combine like terms: -0.003333333334 + 0.003333333334 = 0.000000000000 0.000000000000 + x = -0.044845413 + 0.003333333334 x = -0.044845413 + 0.003333333334 Combine like terms: -0.044845413 + 0.003333333334 = -0.041512079666 x = -0.041512079666 Simplifying x = -0.041512079666Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.048178746334, -0.041512079666}
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