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Simplifying -1.5x2 + 9x + 10.5 = 0 Reorder the terms: 10.5 + 9x + -1.5x2 = 0 Solving 10.5 + 9x + -1.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1.5 the coefficient of the squared term: Divide each side by '-1.5'. -7 + -6x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -6x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -6x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -6x + x2 = 0 + 7 -6x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -6x + x2 = 7 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 7 + 9 Reorder the terms: 9 + -6x + x2 = 7 + 9 Combine like terms: 7 + 9 = 16 9 + -6x + x2 = 16 Factor a perfect square on the left side: (x + -3)(x + -3) = 16 Calculate the square root of the right side: 4 Break this problem into two subproblems by setting (x + -3) equal to 4 and -4.Subproblem 1
x + -3 = 4 Simplifying x + -3 = 4 Reorder the terms: -3 + x = 4 Solving -3 + x = 4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 4 + 3 Combine like terms: -3 + 3 = 0 0 + x = 4 + 3 x = 4 + 3 Combine like terms: 4 + 3 = 7 x = 7 Simplifying x = 7Subproblem 2
x + -3 = -4 Simplifying x + -3 = -4 Reorder the terms: -3 + x = -4 Solving -3 + x = -4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -4 + 3 Combine like terms: -3 + 3 = 0 0 + x = -4 + 3 x = -4 + 3 Combine like terms: -4 + 3 = -1 x = -1 Simplifying x = -1Solution
The solution to the problem is based on the solutions from the subproblems. x = {7, -1}
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