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Simplifying 0 = x2 + -2x + -1.89 Reorder the terms: 0 = -1.89 + -2x + x2 Solving 0 = -1.89 + -2x + x2 Solving for variable 'x'. Combine like terms: 0 + 1.89 = 1.89 1.89 + 2x + -1x2 = -1.89 + -2x + x2 + 1.89 + 2x + -1x2 Reorder the terms: 1.89 + 2x + -1x2 = -1.89 + 1.89 + -2x + 2x + x2 + -1x2 Combine like terms: -1.89 + 1.89 = 0.00 1.89 + 2x + -1x2 = 0.00 + -2x + 2x + x2 + -1x2 1.89 + 2x + -1x2 = -2x + 2x + x2 + -1x2 Combine like terms: -2x + 2x = 0 1.89 + 2x + -1x2 = 0 + x2 + -1x2 1.89 + 2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 1.89 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1.89 + -2x + x2 = 0 Move the constant term to the right: Add '1.89' to each side of the equation. -1.89 + -2x + 1.89 + x2 = 0 + 1.89 Reorder the terms: -1.89 + 1.89 + -2x + x2 = 0 + 1.89 Combine like terms: -1.89 + 1.89 = 0.00 0.00 + -2x + x2 = 0 + 1.89 -2x + x2 = 0 + 1.89 Combine like terms: 0 + 1.89 = 1.89 -2x + x2 = 1.89 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 1.89 + 1 Reorder the terms: 1 + -2x + x2 = 1.89 + 1 Combine like terms: 1.89 + 1 = 2.89 1 + -2x + x2 = 2.89 Factor a perfect square on the left side: (x + -1)(x + -1) = 2.89 Calculate the square root of the right side: 1.7 Break this problem into two subproblems by setting (x + -1) equal to 1.7 and -1.7.Subproblem 1
x + -1 = 1.7 Simplifying x + -1 = 1.7 Reorder the terms: -1 + x = 1.7 Solving -1 + x = 1.7 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.7 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.7 + 1 x = 1.7 + 1 Combine like terms: 1.7 + 1 = 2.7 x = 2.7 Simplifying x = 2.7Subproblem 2
x + -1 = -1.7 Simplifying x + -1 = -1.7 Reorder the terms: -1 + x = -1.7 Solving -1 + x = -1.7 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.7 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.7 + 1 x = -1.7 + 1 Combine like terms: -1.7 + 1 = -0.7 x = -0.7 Simplifying x = -0.7Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.7, -0.7}
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