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Simplifying 0.5x2 + -4x + -10 = 0 Reorder the terms: -10 + -4x + 0.5x2 = 0 Solving -10 + -4x + 0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -20 + -8x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -8x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -8x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -8x + x2 = 0 + 20 -8x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -8x + x2 = 20 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 20 + 16 Reorder the terms: 16 + -8x + x2 = 20 + 16 Combine like terms: 20 + 16 = 36 16 + -8x + x2 = 36 Factor a perfect square on the left side: (x + -4)(x + -4) = 36 Calculate the square root of the right side: 6 Break this problem into two subproblems by setting (x + -4) equal to 6 and -6.Subproblem 1
x + -4 = 6 Simplifying x + -4 = 6 Reorder the terms: -4 + x = 6 Solving -4 + x = 6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 6 + 4 Combine like terms: -4 + 4 = 0 0 + x = 6 + 4 x = 6 + 4 Combine like terms: 6 + 4 = 10 x = 10 Simplifying x = 10Subproblem 2
x + -4 = -6 Simplifying x + -4 = -6 Reorder the terms: -4 + x = -6 Solving -4 + x = -6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -6 + 4 Combine like terms: -4 + 4 = 0 0 + x = -6 + 4 x = -6 + 4 Combine like terms: -6 + 4 = -2 x = -2 Simplifying x = -2Solution
The solution to the problem is based on the solutions from the subproblems. x = {10, -2}
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