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Simplifying -1x2 + 2.5x + 1.5 = 0 Reorder the terms: 1.5 + 2.5x + -1x2 = 0 Solving 1.5 + 2.5x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1.5 + -2.5x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -2.5x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -2.5x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -2.5x + x2 = 0 + 1.5 -2.5x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -2.5x + x2 = 1.5 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 1.5 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 1.5 + 1.5625 Combine like terms: 1.5 + 1.5625 = 3.0625 1.5625 + -2.5x + x2 = 3.0625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 3.0625 Calculate the square root of the right side: 1.75 Break this problem into two subproblems by setting (x + -1.25) equal to 1.75 and -1.75.Subproblem 1
x + -1.25 = 1.75 Simplifying x + -1.25 = 1.75 Reorder the terms: -1.25 + x = 1.75 Solving -1.25 + x = 1.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 1.75 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 1.75 + 1.25 x = 1.75 + 1.25 Combine like terms: 1.75 + 1.25 = 3 x = 3 Simplifying x = 3Subproblem 2
x + -1.25 = -1.75 Simplifying x + -1.25 = -1.75 Reorder the terms: -1.25 + x = -1.75 Solving -1.25 + x = -1.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -1.75 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -1.75 + 1.25 x = -1.75 + 1.25 Combine like terms: -1.75 + 1.25 = -0.5 x = -0.5 Simplifying x = -0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {3, -0.5}
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