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Simplifying 150 = -0.048x2 + 1.87x + 154 Reorder the terms: 150 = 154 + 1.87x + -0.048x2 Solving 150 = 154 + 1.87x + -0.048x2 Solving for variable 'x'. Combine like terms: 150 + -154 = -4 -4 + -1.87x + 0.048x2 = 154 + 1.87x + -0.048x2 + -154 + -1.87x + 0.048x2 Reorder the terms: -4 + -1.87x + 0.048x2 = 154 + -154 + 1.87x + -1.87x + -0.048x2 + 0.048x2 Combine like terms: 154 + -154 = 0 -4 + -1.87x + 0.048x2 = 0 + 1.87x + -1.87x + -0.048x2 + 0.048x2 -4 + -1.87x + 0.048x2 = 1.87x + -1.87x + -0.048x2 + 0.048x2 Combine like terms: 1.87x + -1.87x = 0.00 -4 + -1.87x + 0.048x2 = 0.00 + -0.048x2 + 0.048x2 -4 + -1.87x + 0.048x2 = -0.048x2 + 0.048x2 Combine like terms: -0.048x2 + 0.048x2 = 0.000 -4 + -1.87x + 0.048x2 = 0.000 Begin completing the square. Divide all terms by 0.048 the coefficient of the squared term: Divide each side by '0.048'. -83.33333333 + -38.95833333x + x2 = 0 Move the constant term to the right: Add '83.33333333' to each side of the equation. -83.33333333 + -38.95833333x + 83.33333333 + x2 = 0 + 83.33333333 Reorder the terms: -83.33333333 + 83.33333333 + -38.95833333x + x2 = 0 + 83.33333333 Combine like terms: -83.33333333 + 83.33333333 = 0.00000000 0.00000000 + -38.95833333x + x2 = 0 + 83.33333333 -38.95833333x + x2 = 0 + 83.33333333 Combine like terms: 0 + 83.33333333 = 83.33333333 -38.95833333x + x2 = 83.33333333 The x term is -38.95833333x. Take half its coefficient (-19.47916667). Square it (379.4379342) and add it to both sides. Add '379.4379342' to each side of the equation. -38.95833333x + 379.4379342 + x2 = 83.33333333 + 379.4379342 Reorder the terms: 379.4379342 + -38.95833333x + x2 = 83.33333333 + 379.4379342 Combine like terms: 83.33333333 + 379.4379342 = 462.77126753 379.4379342 + -38.95833333x + x2 = 462.77126753 Factor a perfect square on the left side: (x + -19.47916667)(x + -19.47916667) = 462.77126753 Calculate the square root of the right side: 21.512119085 Break this problem into two subproblems by setting (x + -19.47916667) equal to 21.512119085 and -21.512119085.Subproblem 1
x + -19.47916667 = 21.512119085 Simplifying x + -19.47916667 = 21.512119085 Reorder the terms: -19.47916667 + x = 21.512119085 Solving -19.47916667 + x = 21.512119085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19.47916667' to each side of the equation. -19.47916667 + 19.47916667 + x = 21.512119085 + 19.47916667 Combine like terms: -19.47916667 + 19.47916667 = 0.00000000 0.00000000 + x = 21.512119085 + 19.47916667 x = 21.512119085 + 19.47916667 Combine like terms: 21.512119085 + 19.47916667 = 40.991285755 x = 40.991285755 Simplifying x = 40.991285755Subproblem 2
x + -19.47916667 = -21.512119085 Simplifying x + -19.47916667 = -21.512119085 Reorder the terms: -19.47916667 + x = -21.512119085 Solving -19.47916667 + x = -21.512119085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19.47916667' to each side of the equation. -19.47916667 + 19.47916667 + x = -21.512119085 + 19.47916667 Combine like terms: -19.47916667 + 19.47916667 = 0.00000000 0.00000000 + x = -21.512119085 + 19.47916667 x = -21.512119085 + 19.47916667 Combine like terms: -21.512119085 + 19.47916667 = -2.032952415 x = -2.032952415 Simplifying x = -2.032952415Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.991285755, -2.032952415}
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