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Simplifying 5x2 + 8x + -11 = 0 Reorder the terms: -11 + 8x + 5x2 = 0 Solving -11 + 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'. -2.2 + 1.6x + x2 = 0 Move the constant term to the right: Add '2.2' to each side of the equation. -2.2 + 1.6x + 2.2 + x2 = 0 + 2.2 Reorder the terms: -2.2 + 2.2 + 1.6x + x2 = 0 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + 1.6x + x2 = 0 + 2.2 1.6x + x2 = 0 + 2.2 Combine like terms: 0 + 2.2 = 2.2 1.6x + x2 = 2.2 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 = 2.2 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = 2.2 + 0.64 Combine like terms: 2.2 + 0.64 = 2.84 0.64 + 1.6x + x2 = 2.84 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 2.84 Calculate the square root of the right side: 1.685229955 Break this problem into two subproblems by setting (x + 0.8) equal to 1.685229955 and -1.685229955.Subproblem 1
x + 0.8 = 1.685229955 Simplifying x + 0.8 = 1.685229955 Reorder the terms: 0.8 + x = 1.685229955 Solving 0.8 + x = 1.685229955 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 = 1.685229955 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 1.685229955 + -0.8 x = 1.685229955 + -0.8 Combine like terms: 1.685229955 + -0.8 = 0.885229955 x = 0.885229955 Simplifying x = 0.885229955Subproblem 2
x + 0.8 = -1.685229955 Simplifying x + 0.8 = -1.685229955 Reorder the terms: 0.8 + x = -1.685229955 Solving 0.8 + x = -1.685229955 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 = -1.685229955 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -1.685229955 + -0.8 x = -1.685229955 + -0.8 Combine like terms: -1.685229955 + -0.8 = -2.485229955 x = -2.485229955 Simplifying x = -2.485229955Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.885229955, -2.485229955}
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