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Simplifying 1.5x2 + 6x = 7.5 Reorder the terms: 6x + 1.5x2 = 7.5 Solving 6x + 1.5x2 = 7.5 Solving for variable 'x'. Reorder the terms: -7.5 + 6x + 1.5x2 = 7.5 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 -7.5 + 6x + 1.5x2 = 0.0 Begin completing the square. Divide all terms by 1.5 the coefficient of the squared term: Divide each side by '1.5'. -5 + 4x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 4x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 4x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 4x + x2 = 0 + 5 4x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 4x + x2 = 5 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 = 5 + 4 Reorder the terms: 4 + 4x + x2 = 5 + 4 Combine like terms: 5 + 4 = 9 4 + 4x + x2 = 9 Factor a perfect square on the left side: (x + 2)(x + 2) = 9 Calculate the square root of the right side: 3 Break this problem into two subproblems by setting (x + 2) equal to 3 and -3.Subproblem 1
x + 2 = 3 Simplifying x + 2 = 3 Reorder the terms: 2 + x = 3 Solving 2 + x = 3 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 = 3 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3 + -2 x = 3 + -2 Combine like terms: 3 + -2 = 1 x = 1 Simplifying x = 1Subproblem 2
x + 2 = -3 Simplifying x + 2 = -3 Reorder the terms: 2 + x = -3 Solving 2 + x = -3 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 = -3 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3 + -2 x = -3 + -2 Combine like terms: -3 + -2 = -5 x = -5 Simplifying x = -5Solution
The solution to the problem is based on the solutions from the subproblems. x = {1, -5}
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