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Simplifying 5x + -1.5 + -0.2x2 + -0.25 = 0 Reorder the terms: -1.5 + -0.25 + 5x + -0.2x2 = 0 Combine like terms: -1.5 + -0.25 = -1.75 -1.75 + 5x + -0.2x2 = 0 Solving -1.75 + 5x + -0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. 8.75 + -25x + x2 = 0 Move the constant term to the right: Add '-8.75' to each side of the equation. 8.75 + -25x + -8.75 + x2 = 0 + -8.75 Reorder the terms: 8.75 + -8.75 + -25x + x2 = 0 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + -25x + x2 = 0 + -8.75 -25x + x2 = 0 + -8.75 Combine like terms: 0 + -8.75 = -8.75 -25x + x2 = -8.75 The x term is -25x. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25x + 156.25 + x2 = -8.75 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -8.75 + 156.25 Combine like terms: -8.75 + 156.25 = 147.5 156.25 + -25x + x2 = 147.5 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 147.5 Calculate the square root of the right side: 12.144957801 Break this problem into two subproblems by setting (x + -12.5) equal to 12.144957801 and -12.144957801.Subproblem 1
x + -12.5 = 12.144957801 Simplifying x + -12.5 = 12.144957801 Reorder the terms: -12.5 + x = 12.144957801 Solving -12.5 + x = 12.144957801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = 12.144957801 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 12.144957801 + 12.5 x = 12.144957801 + 12.5 Combine like terms: 12.144957801 + 12.5 = 24.644957801 x = 24.644957801 Simplifying x = 24.644957801Subproblem 2
x + -12.5 = -12.144957801 Simplifying x + -12.5 = -12.144957801 Reorder the terms: -12.5 + x = -12.144957801 Solving -12.5 + x = -12.144957801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = -12.144957801 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -12.144957801 + 12.5 x = -12.144957801 + 12.5 Combine like terms: -12.144957801 + 12.5 = 0.355042199 x = 0.355042199 Simplifying x = 0.355042199Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.644957801, 0.355042199}
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