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Simplifying (-0.5x2) + 1.5x + 9 = 4 Reorder the terms: 9 + 1.5x + (-0.5x2) = 4 Solving 9 + 1.5x + (-0.5x2) = 4 Solving for variable 'x'. Reorder the terms: 9 + -4 + 1.5x + (-0.5x2) = 4 + -4 Combine like terms: 9 + -4 = 5 5 + 1.5x + (-0.5x2) = 4 + -4 Combine like terms: 4 + -4 = 0 5 + 1.5x + (-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'. -10 + -3x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -3x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -3x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -3x + x2 = 0 + 10 -3x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -3x + x2 = 10 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 10 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 10 + 2.25 Combine like terms: 10 + 2.25 = 12.25 2.25 + -3x + x2 = 12.25 Factor a perfect square on the left side: ((x) + -1.5)((x) + -1.5) = 12.25 Calculate the square root of the right side: 3.5 Break this problem into two subproblems by setting ((x) + -1.5) equal to 3.5 and -3.5.Subproblem 1
(x) + -1.5 = 3.5 Simplifying (x) + -1.5 = 3.5 x + -1.5 = 3.5 Reorder the terms: -1.5 + x = 3.5 Solving -1.5 + x = 3.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 3.5 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 3.5 + 1.5 x = 3.5 + 1.5 Combine like terms: 3.5 + 1.5 = 5 x = 5 Simplifying x = 5Subproblem 2
(x) + -1.5 = -3.5 Simplifying (x) + -1.5 = -3.5 x + -1.5 = -3.5 Reorder the terms: -1.5 + x = -3.5 Solving -1.5 + x = -3.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -3.5 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -3.5 + 1.5 x = -3.5 + 1.5 Combine like terms: -3.5 + 1.5 = -2 x = -2 Simplifying x = -2Solution
The solution to the problem is based on the solutions from the subproblems. x = {5, -2}
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