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Simplifying -0.015x2 + 2.38x + -3 = 0 Reorder the terms: -3 + 2.38x + -0.015x2 = 0 Solving -3 + 2.38x + -0.015x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.015 the coefficient of the squared term: Divide each side by '-0.015'. 200 + -158.6666667x + x2 = 0 Move the constant term to the right: Add '-200' to each side of the equation. 200 + -158.6666667x + -200 + x2 = 0 + -200 Reorder the terms: 200 + -200 + -158.6666667x + x2 = 0 + -200 Combine like terms: 200 + -200 = 0 0 + -158.6666667x + x2 = 0 + -200 -158.6666667x + x2 = 0 + -200 Combine like terms: 0 + -200 = -200 -158.6666667x + x2 = -200 The x term is -158.6666667x. Take half its coefficient (-79.33333335). Square it (6293.777780) and add it to both sides. Add '6293.777780' to each side of the equation. -158.6666667x + 6293.777780 + x2 = -200 + 6293.777780 Reorder the terms: 6293.777780 + -158.6666667x + x2 = -200 + 6293.777780 Combine like terms: -200 + 6293.777780 = 6093.77778 6293.777780 + -158.6666667x + x2 = 6093.77778 Factor a perfect square on the left side: (x + -79.33333335)(x + -79.33333335) = 6093.77778 Calculate the square root of the right side: 78.062652914 Break this problem into two subproblems by setting (x + -79.33333335) equal to 78.062652914 and -78.062652914.Subproblem 1
x + -79.33333335 = 78.062652914 Simplifying x + -79.33333335 = 78.062652914 Reorder the terms: -79.33333335 + x = 78.062652914 Solving -79.33333335 + x = 78.062652914 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '79.33333335' to each side of the equation. -79.33333335 + 79.33333335 + x = 78.062652914 + 79.33333335 Combine like terms: -79.33333335 + 79.33333335 = 0.00000000 0.00000000 + x = 78.062652914 + 79.33333335 x = 78.062652914 + 79.33333335 Combine like terms: 78.062652914 + 79.33333335 = 157.395986264 x = 157.395986264 Simplifying x = 157.395986264Subproblem 2
x + -79.33333335 = -78.062652914 Simplifying x + -79.33333335 = -78.062652914 Reorder the terms: -79.33333335 + x = -78.062652914 Solving -79.33333335 + x = -78.062652914 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '79.33333335' to each side of the equation. -79.33333335 + 79.33333335 + x = -78.062652914 + 79.33333335 Combine like terms: -79.33333335 + 79.33333335 = 0.00000000 0.00000000 + x = -78.062652914 + 79.33333335 x = -78.062652914 + 79.33333335 Combine like terms: -78.062652914 + 79.33333335 = 1.270680436 x = 1.270680436 Simplifying x = 1.270680436Solution
The solution to the problem is based on the solutions from the subproblems. x = {157.395986264, 1.270680436}
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