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Simplifying 200x + -0.3x2 + -0.1x2 + 24x + 284 = 0 Reorder the terms: 284 + 200x + 24x + -0.3x2 + -0.1x2 = 0 Combine like terms: 200x + 24x = 224x 284 + 224x + -0.3x2 + -0.1x2 = 0 Combine like terms: -0.3x2 + -0.1x2 = -0.4x2 284 + 224x + -0.4x2 = 0 Solving 284 + 224x + -0.4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.4 the coefficient of the squared term: Divide each side by '-0.4'. -710 + -560x + x2 = 0 Move the constant term to the right: Add '710' to each side of the equation. -710 + -560x + 710 + x2 = 0 + 710 Reorder the terms: -710 + 710 + -560x + x2 = 0 + 710 Combine like terms: -710 + 710 = 0 0 + -560x + x2 = 0 + 710 -560x + x2 = 0 + 710 Combine like terms: 0 + 710 = 710 -560x + x2 = 710 The x term is -560x. Take half its coefficient (-280). Square it (78400) and add it to both sides. Add '78400' to each side of the equation. -560x + 78400 + x2 = 710 + 78400 Reorder the terms: 78400 + -560x + x2 = 710 + 78400 Combine like terms: 710 + 78400 = 79110 78400 + -560x + x2 = 79110 Factor a perfect square on the left side: (x + -280)(x + -280) = 79110 Calculate the square root of the right side: 281.2649996 Break this problem into two subproblems by setting (x + -280) equal to 281.2649996 and -281.2649996.Subproblem 1
x + -280 = 281.2649996 Simplifying x + -280 = 281.2649996 Reorder the terms: -280 + x = 281.2649996 Solving -280 + x = 281.2649996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '280' to each side of the equation. -280 + 280 + x = 281.2649996 + 280 Combine like terms: -280 + 280 = 0 0 + x = 281.2649996 + 280 x = 281.2649996 + 280 Combine like terms: 281.2649996 + 280 = 561.2649996 x = 561.2649996 Simplifying x = 561.2649996Subproblem 2
x + -280 = -281.2649996 Simplifying x + -280 = -281.2649996 Reorder the terms: -280 + x = -281.2649996 Solving -280 + x = -281.2649996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '280' to each side of the equation. -280 + 280 + x = -281.2649996 + 280 Combine like terms: -280 + 280 = 0 0 + x = -281.2649996 + 280 x = -281.2649996 + 280 Combine like terms: -281.2649996 + 280 = -1.2649996 x = -1.2649996 Simplifying x = -1.2649996Solution
The solution to the problem is based on the solutions from the subproblems. x = {561.2649996, -1.2649996}
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