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Simplifying 143x + -8x2 = 600 Solving 143x + -8x2 = 600 Solving for variable 'x'. Reorder the terms: -600 + 143x + -8x2 = 600 + -600 Combine like terms: 600 + -600 = 0 -600 + 143x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 75 + -17.875x + x2 = 0 Move the constant term to the right: Add '-75' to each side of the equation. 75 + -17.875x + -75 + x2 = 0 + -75 Reorder the terms: 75 + -75 + -17.875x + x2 = 0 + -75 Combine like terms: 75 + -75 = 0 0 + -17.875x + x2 = 0 + -75 -17.875x + x2 = 0 + -75 Combine like terms: 0 + -75 = -75 -17.875x + x2 = -75 The x term is -17.875x. Take half its coefficient (-8.9375). Square it (79.87890625) and add it to both sides. Add '79.87890625' to each side of the equation. -17.875x + 79.87890625 + x2 = -75 + 79.87890625 Reorder the terms: 79.87890625 + -17.875x + x2 = -75 + 79.87890625 Combine like terms: -75 + 79.87890625 = 4.87890625 79.87890625 + -17.875x + x2 = 4.87890625 Factor a perfect square on the left side: (x + -8.9375)(x + -8.9375) = 4.87890625 Calculate the square root of the right side: 2.208824631 Break this problem into two subproblems by setting (x + -8.9375) equal to 2.208824631 and -2.208824631.Subproblem 1
x + -8.9375 = 2.208824631 Simplifying x + -8.9375 = 2.208824631 Reorder the terms: -8.9375 + x = 2.208824631 Solving -8.9375 + x = 2.208824631 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.9375' to each side of the equation. -8.9375 + 8.9375 + x = 2.208824631 + 8.9375 Combine like terms: -8.9375 + 8.9375 = 0.0000 0.0000 + x = 2.208824631 + 8.9375 x = 2.208824631 + 8.9375 Combine like terms: 2.208824631 + 8.9375 = 11.146324631 x = 11.146324631 Simplifying x = 11.146324631Subproblem 2
x + -8.9375 = -2.208824631 Simplifying x + -8.9375 = -2.208824631 Reorder the terms: -8.9375 + x = -2.208824631 Solving -8.9375 + x = -2.208824631 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.9375' to each side of the equation. -8.9375 + 8.9375 + x = -2.208824631 + 8.9375 Combine like terms: -8.9375 + 8.9375 = 0.0000 0.0000 + x = -2.208824631 + 8.9375 x = -2.208824631 + 8.9375 Combine like terms: -2.208824631 + 8.9375 = 6.728675369 x = 6.728675369 Simplifying x = 6.728675369Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.146324631, 6.728675369}
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