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Simplifying 0.08x2 + -24x + 250 = 570 Reorder the terms: 250 + -24x + 0.08x2 = 570 Solving 250 + -24x + 0.08x2 = 570 Solving for variable 'x'. Reorder the terms: 250 + -570 + -24x + 0.08x2 = 570 + -570 Combine like terms: 250 + -570 = -320 -320 + -24x + 0.08x2 = 570 + -570 Combine like terms: 570 + -570 = 0 -320 + -24x + 0.08x2 = 0 Begin completing the square. Divide all terms by 0.08 the coefficient of the squared term: Divide each side by '0.08'. -4000 + -300x + x2 = 0 Move the constant term to the right: Add '4000' to each side of the equation. -4000 + -300x + 4000 + x2 = 0 + 4000 Reorder the terms: -4000 + 4000 + -300x + x2 = 0 + 4000 Combine like terms: -4000 + 4000 = 0 0 + -300x + x2 = 0 + 4000 -300x + x2 = 0 + 4000 Combine like terms: 0 + 4000 = 4000 -300x + x2 = 4000 The x term is -300x. Take half its coefficient (-150). Square it (22500) and add it to both sides. Add '22500' to each side of the equation. -300x + 22500 + x2 = 4000 + 22500 Reorder the terms: 22500 + -300x + x2 = 4000 + 22500 Combine like terms: 4000 + 22500 = 26500 22500 + -300x + x2 = 26500 Factor a perfect square on the left side: (x + -150)(x + -150) = 26500 Calculate the square root of the right side: 162.788205961 Break this problem into two subproblems by setting (x + -150) equal to 162.788205961 and -162.788205961.Subproblem 1
x + -150 = 162.788205961 Simplifying x + -150 = 162.788205961 Reorder the terms: -150 + x = 162.788205961 Solving -150 + x = 162.788205961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '150' to each side of the equation. -150 + 150 + x = 162.788205961 + 150 Combine like terms: -150 + 150 = 0 0 + x = 162.788205961 + 150 x = 162.788205961 + 150 Combine like terms: 162.788205961 + 150 = 312.788205961 x = 312.788205961 Simplifying x = 312.788205961Subproblem 2
x + -150 = -162.788205961 Simplifying x + -150 = -162.788205961 Reorder the terms: -150 + x = -162.788205961 Solving -150 + x = -162.788205961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '150' to each side of the equation. -150 + 150 + x = -162.788205961 + 150 Combine like terms: -150 + 150 = 0 0 + x = -162.788205961 + 150 x = -162.788205961 + 150 Combine like terms: -162.788205961 + 150 = -12.788205961 x = -12.788205961 Simplifying x = -12.788205961Solution
The solution to the problem is based on the solutions from the subproblems. x = {312.788205961, -12.788205961}
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