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Simplifying 5x2 + 8x + -100 = 0 Reorder the terms: -100 + 8x + 5x2 = 0 Solving -100 + 8x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -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 = 3.743126677 x = 3.743126677 Simplifying x = 3.743126677Subproblem 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 = -5.343126677 x = -5.343126677 Simplifying x = -5.343126677Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.743126677, -5.343126677}
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