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Simplifying 0.5 + 5x + -2 = x2 Reorder the terms: 0.5 + -2 + 5x = x2 Combine like terms: 0.5 + -2 = -1.5 -1.5 + 5x = x2 Solving -1.5 + 5x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 -1.5 + 5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1.5 + -5x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -5x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -5x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -5x + x2 = 0 + -1.5 -5x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -5x + x2 = -1.5 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -1.5 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -1.5 + 6.25 Combine like terms: -1.5 + 6.25 = 4.75 6.25 + -5x + x2 = 4.75 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (x + -2.5) equal to 2.179449472 and -2.179449472.Subproblem 1
x + -2.5 = 2.179449472 Simplifying x + -2.5 = 2.179449472 Reorder the terms: -2.5 + x = 2.179449472 Solving -2.5 + x = 2.179449472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.179449472 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.179449472 + 2.5 x = 2.179449472 + 2.5 Combine like terms: 2.179449472 + 2.5 = 4.679449472 x = 4.679449472 Simplifying x = 4.679449472Subproblem 2
x + -2.5 = -2.179449472 Simplifying x + -2.5 = -2.179449472 Reorder the terms: -2.5 + x = -2.179449472 Solving -2.5 + x = -2.179449472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.179449472 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.179449472 + 2.5 x = -2.179449472 + 2.5 Combine like terms: -2.179449472 + 2.5 = 0.320550528 x = 0.320550528 Simplifying x = 0.320550528Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.679449472, 0.320550528}
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