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Simplifying -5x2 + 2x = -2 Reorder the terms: 2x + -5x2 = -2 Solving 2x + -5x2 = -2 Solving for variable 'x'. Reorder the terms: 2 + 2x + -5x2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + 2x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.4 + -0.4x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -0.4x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -0.4x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -0.4x + x2 = 0 + 0.4 -0.4x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -0.4x + x2 = 0.4 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = 0.4 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 0.4 + 0.04 Combine like terms: 0.4 + 0.04 = 0.44 0.04 + -0.4x + x2 = 0.44 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 0.44 Calculate the square root of the right side: 0.663324958 Break this problem into two subproblems by setting (x + -0.2) equal to 0.663324958 and -0.663324958.Subproblem 1
x + -0.2 = 0.663324958 Simplifying x + -0.2 = 0.663324958 Reorder the terms: -0.2 + x = 0.663324958 Solving -0.2 + x = 0.663324958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 0.663324958 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 0.663324958 + 0.2 x = 0.663324958 + 0.2 Combine like terms: 0.663324958 + 0.2 = 0.863324958 x = 0.863324958 Simplifying x = 0.863324958Subproblem 2
x + -0.2 = -0.663324958 Simplifying x + -0.2 = -0.663324958 Reorder the terms: -0.2 + x = -0.663324958 Solving -0.2 + x = -0.663324958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -0.663324958 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -0.663324958 + 0.2 x = -0.663324958 + 0.2 Combine like terms: -0.663324958 + 0.2 = -0.463324958 x = -0.463324958 Simplifying x = -0.463324958Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.863324958, -0.463324958}
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