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Simplifying 9.8x + 19.6 = 7500x2 Reorder the terms: 19.6 + 9.8x = 7500x2 Solving 19.6 + 9.8x = 7500x2 Solving for variable 'x'. Combine like terms: 7500x2 + -7500x2 = 0 19.6 + 9.8x + -7500x2 = 0 Begin completing the square. Divide all terms by -7500 the coefficient of the squared term: Divide each side by '-7500'. -0.002613333333 + -0.001306666667x + x2 = 0 Move the constant term to the right: Add '0.002613333333' to each side of the equation. -0.002613333333 + -0.001306666667x + 0.002613333333 + x2 = 0 + 0.002613333333 Reorder the terms: -0.002613333333 + 0.002613333333 + -0.001306666667x + x2 = 0 + 0.002613333333 Combine like terms: -0.002613333333 + 0.002613333333 = 0.000000000000 0.000000000000 + -0.001306666667x + x2 = 0 + 0.002613333333 -0.001306666667x + x2 = 0 + 0.002613333333 Combine like terms: 0 + 0.002613333333 = 0.002613333333 -0.001306666667x + x2 = 0.002613333333 The x term is -0.001306666667x. Take half its coefficient (-0.0006533333335). Square it (0.0000004268444447) and add it to both sides. Add '0.0000004268444447' to each side of the equation. -0.001306666667x + 0.0000004268444447 + x2 = 0.002613333333 + 0.0000004268444447 Reorder the terms: 0.0000004268444447 + -0.001306666667x + x2 = 0.002613333333 + 0.0000004268444447 Combine like terms: 0.002613333333 + 0.0000004268444447 = 0.0026137601774447 0.0000004268444447 + -0.001306666667x + x2 = 0.0026137601774447 Factor a perfect square on the left side: (x + -0.0006533333335)(x + -0.0006533333335) = 0.0026137601774447 Calculate the square root of the right side: 0.051124947 Break this problem into two subproblems by setting (x + -0.0006533333335) equal to 0.051124947 and -0.051124947.Subproblem 1
x + -0.0006533333335 = 0.051124947 Simplifying x + -0.0006533333335 = 0.051124947 Reorder the terms: -0.0006533333335 + x = 0.051124947 Solving -0.0006533333335 + x = 0.051124947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0006533333335' to each side of the equation. -0.0006533333335 + 0.0006533333335 + x = 0.051124947 + 0.0006533333335 Combine like terms: -0.0006533333335 + 0.0006533333335 = 0.0000000000000 0.0000000000000 + x = 0.051124947 + 0.0006533333335 x = 0.051124947 + 0.0006533333335 Combine like terms: 0.051124947 + 0.0006533333335 = 0.0517782803335 x = 0.0517782803335 Simplifying x = 0.0517782803335Subproblem 2
x + -0.0006533333335 = -0.051124947 Simplifying x + -0.0006533333335 = -0.051124947 Reorder the terms: -0.0006533333335 + x = -0.051124947 Solving -0.0006533333335 + x = -0.051124947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0006533333335' to each side of the equation. -0.0006533333335 + 0.0006533333335 + x = -0.051124947 + 0.0006533333335 Combine like terms: -0.0006533333335 + 0.0006533333335 = 0.0000000000000 0.0000000000000 + x = -0.051124947 + 0.0006533333335 x = -0.051124947 + 0.0006533333335 Combine like terms: -0.051124947 + 0.0006533333335 = -0.0504716136665 x = -0.0504716136665 Simplifying x = -0.0504716136665Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0517782803335, -0.0504716136665}
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