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Simplifying x2 + 1.88x + -1.18 = 0 Reorder the terms: -1.18 + 1.88x + x2 = 0 Solving -1.18 + 1.88x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1.18' to each side of the equation. -1.18 + 1.88x + 1.18 + x2 = 0 + 1.18 Reorder the terms: -1.18 + 1.18 + 1.88x + x2 = 0 + 1.18 Combine like terms: -1.18 + 1.18 = 0.00 0.00 + 1.88x + x2 = 0 + 1.18 1.88x + x2 = 0 + 1.18 Combine like terms: 0 + 1.18 = 1.18 1.88x + x2 = 1.18 The x term is 1.88x. Take half its coefficient (0.94). Square it (0.8836) and add it to both sides. Add '0.8836' to each side of the equation. 1.88x + 0.8836 + x2 = 1.18 + 0.8836 Reorder the terms: 0.8836 + 1.88x + x2 = 1.18 + 0.8836 Combine like terms: 1.18 + 0.8836 = 2.0636 0.8836 + 1.88x + x2 = 2.0636 Factor a perfect square on the left side: (x + 0.94)(x + 0.94) = 2.0636 Calculate the square root of the right side: 1.436523581 Break this problem into two subproblems by setting (x + 0.94) equal to 1.436523581 and -1.436523581.Subproblem 1
x + 0.94 = 1.436523581 Simplifying x + 0.94 = 1.436523581 Reorder the terms: 0.94 + x = 1.436523581 Solving 0.94 + x = 1.436523581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.94' to each side of the equation. 0.94 + -0.94 + x = 1.436523581 + -0.94 Combine like terms: 0.94 + -0.94 = 0.00 0.00 + x = 1.436523581 + -0.94 x = 1.436523581 + -0.94 Combine like terms: 1.436523581 + -0.94 = 0.496523581 x = 0.496523581 Simplifying x = 0.496523581Subproblem 2
x + 0.94 = -1.436523581 Simplifying x + 0.94 = -1.436523581 Reorder the terms: 0.94 + x = -1.436523581 Solving 0.94 + x = -1.436523581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.94' to each side of the equation. 0.94 + -0.94 + x = -1.436523581 + -0.94 Combine like terms: 0.94 + -0.94 = 0.00 0.00 + x = -1.436523581 + -0.94 x = -1.436523581 + -0.94 Combine like terms: -1.436523581 + -0.94 = -2.376523581 x = -2.376523581 Simplifying x = -2.376523581Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.496523581, -2.376523581}
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