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Simplifying 0.5x2 + 4x + -10 = x + 2 Reorder the terms: -10 + 4x + 0.5x2 = x + 2 Reorder the terms: -10 + 4x + 0.5x2 = 2 + x Solving -10 + 4x + 0.5x2 = 2 + x Solving for variable 'x'. Reorder the terms: -10 + -2 + 4x + -1x + 0.5x2 = 2 + x + -2 + -1x Combine like terms: -10 + -2 = -12 -12 + 4x + -1x + 0.5x2 = 2 + x + -2 + -1x Combine like terms: 4x + -1x = 3x -12 + 3x + 0.5x2 = 2 + x + -2 + -1x Reorder the terms: -12 + 3x + 0.5x2 = 2 + -2 + x + -1x Combine like terms: 2 + -2 = 0 -12 + 3x + 0.5x2 = 0 + x + -1x -12 + 3x + 0.5x2 = x + -1x Combine like terms: x + -1x = 0 -12 + 3x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -24 + 6x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + 6x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 6x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 6x + x2 = 0 + 24 6x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 6x + x2 = 24 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 24 + 9 Reorder the terms: 9 + 6x + x2 = 24 + 9 Combine like terms: 24 + 9 = 33 9 + 6x + x2 = 33 Factor a perfect square on the left side: (x + 3)(x + 3) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (x + 3) equal to 5.744562647 and -5.744562647.Subproblem 1
x + 3 = 5.744562647 Simplifying x + 3 = 5.744562647 Reorder the terms: 3 + x = 5.744562647 Solving 3 + x = 5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 5.744562647 + -3 Combine like terms: 3 + -3 = 0 0 + x = 5.744562647 + -3 x = 5.744562647 + -3 Combine like terms: 5.744562647 + -3 = 2.744562647 x = 2.744562647 Simplifying x = 2.744562647Subproblem 2
x + 3 = -5.744562647 Simplifying x + 3 = -5.744562647 Reorder the terms: 3 + x = -5.744562647 Solving 3 + x = -5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -5.744562647 + -3 Combine like terms: 3 + -3 = 0 0 + x = -5.744562647 + -3 x = -5.744562647 + -3 Combine like terms: -5.744562647 + -3 = -8.744562647 x = -8.744562647 Simplifying x = -8.744562647Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.744562647, -8.744562647}
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