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Simplifying 50 = -0.006x2 + 1.2x + 10 Reorder the terms: 50 = 10 + 1.2x + -0.006x2 Solving 50 = 10 + 1.2x + -0.006x2 Solving for variable 'x'. Combine like terms: 50 + -10 = 40 40 + -1.2x + 0.006x2 = 10 + 1.2x + -0.006x2 + -10 + -1.2x + 0.006x2 Reorder the terms: 40 + -1.2x + 0.006x2 = 10 + -10 + 1.2x + -1.2x + -0.006x2 + 0.006x2 Combine like terms: 10 + -10 = 0 40 + -1.2x + 0.006x2 = 0 + 1.2x + -1.2x + -0.006x2 + 0.006x2 40 + -1.2x + 0.006x2 = 1.2x + -1.2x + -0.006x2 + 0.006x2 Combine like terms: 1.2x + -1.2x = 0.0 40 + -1.2x + 0.006x2 = 0.0 + -0.006x2 + 0.006x2 40 + -1.2x + 0.006x2 = -0.006x2 + 0.006x2 Combine like terms: -0.006x2 + 0.006x2 = 0.000 40 + -1.2x + 0.006x2 = 0.000 Begin completing the square. Divide all terms by 0.006 the coefficient of the squared term: Divide each side by '0.006'. 6666.666667 + -200x + x2 = 0 Move the constant term to the right: Add '-6666.666667' to each side of the equation. 6666.666667 + -200x + -6666.666667 + x2 = 0 + -6666.666667 Reorder the terms: 6666.666667 + -6666.666667 + -200x + x2 = 0 + -6666.666667 Combine like terms: 6666.666667 + -6666.666667 = 0.000000 0.000000 + -200x + x2 = 0 + -6666.666667 -200x + x2 = 0 + -6666.666667 Combine like terms: 0 + -6666.666667 = -6666.666667 -200x + x2 = -6666.666667 The x term is -200x. Take half its coefficient (-100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. -200x + 10000 + x2 = -6666.666667 + 10000 Reorder the terms: 10000 + -200x + x2 = -6666.666667 + 10000 Combine like terms: -6666.666667 + 10000 = 3333.333333 10000 + -200x + x2 = 3333.333333 Factor a perfect square on the left side: (x + -100)(x + -100) = 3333.333333 Calculate the square root of the right side: 57.735026916 Break this problem into two subproblems by setting (x + -100) equal to 57.735026916 and -57.735026916.Subproblem 1
x + -100 = 57.735026916 Simplifying x + -100 = 57.735026916 Reorder the terms: -100 + x = 57.735026916 Solving -100 + x = 57.735026916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = 57.735026916 + 100 Combine like terms: -100 + 100 = 0 0 + x = 57.735026916 + 100 x = 57.735026916 + 100 Combine like terms: 57.735026916 + 100 = 157.735026916 x = 157.735026916 Simplifying x = 157.735026916Subproblem 2
x + -100 = -57.735026916 Simplifying x + -100 = -57.735026916 Reorder the terms: -100 + x = -57.735026916 Solving -100 + x = -57.735026916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = -57.735026916 + 100 Combine like terms: -100 + 100 = 0 0 + x = -57.735026916 + 100 x = -57.735026916 + 100 Combine like terms: -57.735026916 + 100 = 42.264973084 x = 42.264973084 Simplifying x = 42.264973084Solution
The solution to the problem is based on the solutions from the subproblems. x = {157.735026916, 42.264973084}
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