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Simplifying -2x2 + -0.5x + -4 = 4.2x + -5 Reorder the terms: -4 + -0.5x + -2x2 = 4.2x + -5 Reorder the terms: -4 + -0.5x + -2x2 = -5 + 4.2x Solving -4 + -0.5x + -2x2 = -5 + 4.2x Solving for variable 'x'. Reorder the terms: -4 + 5 + -0.5x + -4.2x + -2x2 = -5 + 4.2x + 5 + -4.2x Combine like terms: -4 + 5 = 1 1 + -0.5x + -4.2x + -2x2 = -5 + 4.2x + 5 + -4.2x Combine like terms: -0.5x + -4.2x = -4.7x 1 + -4.7x + -2x2 = -5 + 4.2x + 5 + -4.2x Reorder the terms: 1 + -4.7x + -2x2 = -5 + 5 + 4.2x + -4.2x Combine like terms: -5 + 5 = 0 1 + -4.7x + -2x2 = 0 + 4.2x + -4.2x 1 + -4.7x + -2x2 = 4.2x + -4.2x Combine like terms: 4.2x + -4.2x = 0.0 1 + -4.7x + -2x2 = 0.0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -0.5 + 2.35x + x2 = 0.0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 2.35x + 0.5 + x2 = 0.0 + 0.5 Reorder the terms: -0.5 + 0.5 + 2.35x + x2 = 0.0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 2.35x + x2 = 0.0 + 0.5 2.35x + x2 = 0.0 + 0.5 Combine like terms: 0.0 + 0.5 = 0.5 2.35x + x2 = 0.5 The x term is 2.35x. Take half its coefficient (1.175). Square it (1.380625) and add it to both sides. Add '1.380625' to each side of the equation. 2.35x + 1.380625 + x2 = 0.5 + 1.380625 Reorder the terms: 1.380625 + 2.35x + x2 = 0.5 + 1.380625 Combine like terms: 0.5 + 1.380625 = 1.880625 1.380625 + 2.35x + x2 = 1.880625 Factor a perfect square on the left side: (x + 1.175)(x + 1.175) = 1.880625 Calculate the square root of the right side: 1.371358815 Break this problem into two subproblems by setting (x + 1.175) equal to 1.371358815 and -1.371358815.Subproblem 1
x + 1.175 = 1.371358815 Simplifying x + 1.175 = 1.371358815 Reorder the terms: 1.175 + x = 1.371358815 Solving 1.175 + x = 1.371358815 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.175' to each side of the equation. 1.175 + -1.175 + x = 1.371358815 + -1.175 Combine like terms: 1.175 + -1.175 = 0.000 0.000 + x = 1.371358815 + -1.175 x = 1.371358815 + -1.175 Combine like terms: 1.371358815 + -1.175 = 0.196358815 x = 0.196358815 Simplifying x = 0.196358815Subproblem 2
x + 1.175 = -1.371358815 Simplifying x + 1.175 = -1.371358815 Reorder the terms: 1.175 + x = -1.371358815 Solving 1.175 + x = -1.371358815 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.175' to each side of the equation. 1.175 + -1.175 + x = -1.371358815 + -1.175 Combine like terms: 1.175 + -1.175 = 0.000 0.000 + x = -1.371358815 + -1.175 x = -1.371358815 + -1.175 Combine like terms: -1.371358815 + -1.175 = -2.546358815 x = -2.546358815 Simplifying x = -2.546358815Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.196358815, -2.546358815}
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