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Simplifying 0 = 1.25x2 + -2x + -25 Reorder the terms: 0 = -25 + -2x + 1.25x2 Solving 0 = -25 + -2x + 1.25x2 Solving for variable 'x'. Combine like terms: 0 + 25 = 25 25 + 2x + -1.25x2 = -25 + -2x + 1.25x2 + 25 + 2x + -1.25x2 Reorder the terms: 25 + 2x + -1.25x2 = -25 + 25 + -2x + 2x + 1.25x2 + -1.25x2 Combine like terms: -25 + 25 = 0 25 + 2x + -1.25x2 = 0 + -2x + 2x + 1.25x2 + -1.25x2 25 + 2x + -1.25x2 = -2x + 2x + 1.25x2 + -1.25x2 Combine like terms: -2x + 2x = 0 25 + 2x + -1.25x2 = 0 + 1.25x2 + -1.25x2 25 + 2x + -1.25x2 = 1.25x2 + -1.25x2 Combine like terms: 1.25x2 + -1.25x2 = 0.00 25 + 2x + -1.25x2 = 0.00 Begin completing the square. Divide all terms by -1.25 the coefficient of the squared term: Divide each side by '-1.25'. -20 + -1.6x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -1.6x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -1.6x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -1.6x + x2 = 0 + 20 -1.6x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -1.6x + x2 = 20 The x term is -1.6x. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6x + 0.64 + x2 = 20 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = 20 + 0.64 Combine like terms: 20 + 0.64 = 20.64 0.64 + -1.6x + x2 = 20.64 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 20.64 Calculate the square root of the right side: 4.543126677 Break this problem into two subproblems by setting (x + -0.8) equal to 4.543126677 and -4.543126677.Subproblem 1
x + -0.8 = 4.543126677 Simplifying x + -0.8 = 4.543126677 Reorder the terms: -0.8 + x = 4.543126677 Solving -0.8 + x = 4.543126677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 4.543126677 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 4.543126677 + 0.8 x = 4.543126677 + 0.8 Combine like terms: 4.543126677 + 0.8 = 5.343126677 x = 5.343126677 Simplifying x = 5.343126677Subproblem 2
x + -0.8 = -4.543126677 Simplifying x + -0.8 = -4.543126677 Reorder the terms: -0.8 + x = -4.543126677 Solving -0.8 + x = -4.543126677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = -4.543126677 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -4.543126677 + 0.8 x = -4.543126677 + 0.8 Combine like terms: -4.543126677 + 0.8 = -3.743126677 x = -3.743126677 Simplifying x = -3.743126677Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.343126677, -3.743126677}
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