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Simplifying x2 + 1.32x + -11.81 = 0 Reorder the terms: -11.81 + 1.32x + x2 = 0 Solving -11.81 + 1.32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '11.81' to each side of the equation. -11.81 + 1.32x + 11.81 + x2 = 0 + 11.81 Reorder the terms: -11.81 + 11.81 + 1.32x + x2 = 0 + 11.81 Combine like terms: -11.81 + 11.81 = 0.00 0.00 + 1.32x + x2 = 0 + 11.81 1.32x + x2 = 0 + 11.81 Combine like terms: 0 + 11.81 = 11.81 1.32x + x2 = 11.81 The x term is 1.32x. Take half its coefficient (0.66). Square it (0.4356) and add it to both sides. Add '0.4356' to each side of the equation. 1.32x + 0.4356 + x2 = 11.81 + 0.4356 Reorder the terms: 0.4356 + 1.32x + x2 = 11.81 + 0.4356 Combine like terms: 11.81 + 0.4356 = 12.2456 0.4356 + 1.32x + x2 = 12.2456 Factor a perfect square on the left side: (x + 0.66)(x + 0.66) = 12.2456 Calculate the square root of the right side: 3.499371372 Break this problem into two subproblems by setting (x + 0.66) equal to 3.499371372 and -3.499371372.Subproblem 1
x + 0.66 = 3.499371372 Simplifying x + 0.66 = 3.499371372 Reorder the terms: 0.66 + x = 3.499371372 Solving 0.66 + x = 3.499371372 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.66' to each side of the equation. 0.66 + -0.66 + x = 3.499371372 + -0.66 Combine like terms: 0.66 + -0.66 = 0.00 0.00 + x = 3.499371372 + -0.66 x = 3.499371372 + -0.66 Combine like terms: 3.499371372 + -0.66 = 2.839371372 x = 2.839371372 Simplifying x = 2.839371372Subproblem 2
x + 0.66 = -3.499371372 Simplifying x + 0.66 = -3.499371372 Reorder the terms: 0.66 + x = -3.499371372 Solving 0.66 + x = -3.499371372 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.66' to each side of the equation. 0.66 + -0.66 + x = -3.499371372 + -0.66 Combine like terms: 0.66 + -0.66 = 0.00 0.00 + x = -3.499371372 + -0.66 x = -3.499371372 + -0.66 Combine like terms: -3.499371372 + -0.66 = -4.159371372 x = -4.159371372 Simplifying x = -4.159371372Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.839371372, -4.159371372}
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