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Simplifying -0.5(x2 + 4x + -21) = 0 Reorder the terms: -0.5(-21 + 4x + x2) = 0 (-21 * -0.5 + 4x * -0.5 + x2 * -0.5) = 0 (10.5 + -2x + -0.5x2) = 0 Solving 10.5 + -2x + -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'. -21 + 4x + x2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + 4x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + 4x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 4x + x2 = 0 + 21 4x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 4x + x2 = 21 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 21 + 4 Reorder the terms: 4 + 4x + x2 = 21 + 4 Combine like terms: 21 + 4 = 25 4 + 4x + x2 = 25 Factor a perfect square on the left side: (x + 2)(x + 2) = 25 Calculate the square root of the right side: 5 Break this problem into two subproblems by setting (x + 2) equal to 5 and -5.Subproblem 1
x + 2 = 5 Simplifying x + 2 = 5 Reorder the terms: 2 + x = 5 Solving 2 + x = 5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 5 + -2 Combine like terms: 2 + -2 = 0 0 + x = 5 + -2 x = 5 + -2 Combine like terms: 5 + -2 = 3 x = 3 Simplifying x = 3Subproblem 2
x + 2 = -5 Simplifying x + 2 = -5 Reorder the terms: 2 + x = -5 Solving 2 + x = -5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -5 + -2 Combine like terms: 2 + -2 = 0 0 + x = -5 + -2 x = -5 + -2 Combine like terms: -5 + -2 = -7 x = -7 Simplifying x = -7Solution
The solution to the problem is based on the solutions from the subproblems. x = {3, -7}
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