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Simplifying -0.5x2 + 4x + -7.5 = 0 Reorder the terms: -7.5 + 4x + -0.5x2 = 0 Solving -7.5 + 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'. 15 + -8x + x2 = 0 Move the constant term to the right: Add '-15' to each side of the equation. 15 + -8x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + -8x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -8x + x2 = 0 + -15 -8x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 -8x + x2 = -15 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 = -15 + 16 Reorder the terms: 16 + -8x + x2 = -15 + 16 Combine like terms: -15 + 16 = 1 16 + -8x + x2 = 1 Factor a perfect square on the left side: (x + -4)(x + -4) = 1 Calculate the square root of the right side: 1 Break this problem into two subproblems by setting (x + -4) equal to 1 and -1.Subproblem 1
x + -4 = 1 Simplifying x + -4 = 1 Reorder the terms: -4 + x = 1 Solving -4 + x = 1 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 = 1 + 4 Combine like terms: -4 + 4 = 0 0 + x = 1 + 4 x = 1 + 4 Combine like terms: 1 + 4 = 5 x = 5 Simplifying x = 5Subproblem 2
x + -4 = -1 Simplifying x + -4 = -1 Reorder the terms: -4 + x = -1 Solving -4 + x = -1 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 = -1 + 4 Combine like terms: -4 + 4 = 0 0 + x = -1 + 4 x = -1 + 4 Combine like terms: -1 + 4 = 3 x = 3 Simplifying x = 3Solution
The solution to the problem is based on the solutions from the subproblems. x = {5, 3}
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