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Simplifying 5.6 + -1.5x + -1x2 = 0 Solving 5.6 + -1.5x + -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'. -5.6 + 1.5x + x2 = 0 Move the constant term to the right: Add '5.6' to each side of the equation. -5.6 + 1.5x + 5.6 + x2 = 0 + 5.6 Reorder the terms: -5.6 + 5.6 + 1.5x + x2 = 0 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + 1.5x + x2 = 0 + 5.6 1.5x + x2 = 0 + 5.6 Combine like terms: 0 + 5.6 = 5.6 1.5x + x2 = 5.6 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 5.6 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 5.6 + 0.5625 Combine like terms: 5.6 + 0.5625 = 6.1625 0.5625 + 1.5x + x2 = 6.1625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 6.1625 Calculate the square root of the right side: 2.482438317 Break this problem into two subproblems by setting (x + 0.75) equal to 2.482438317 and -2.482438317.Subproblem 1
x + 0.75 = 2.482438317 Simplifying x + 0.75 = 2.482438317 Reorder the terms: 0.75 + x = 2.482438317 Solving 0.75 + x = 2.482438317 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 2.482438317 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 2.482438317 + -0.75 x = 2.482438317 + -0.75 Combine like terms: 2.482438317 + -0.75 = 1.732438317 x = 1.732438317 Simplifying x = 1.732438317Subproblem 2
x + 0.75 = -2.482438317 Simplifying x + 0.75 = -2.482438317 Reorder the terms: 0.75 + x = -2.482438317 Solving 0.75 + x = -2.482438317 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -2.482438317 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -2.482438317 + -0.75 x = -2.482438317 + -0.75 Combine like terms: -2.482438317 + -0.75 = -3.232438317 x = -3.232438317 Simplifying x = -3.232438317Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.732438317, -3.232438317}
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