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Simplifying -1x2 + 2x + -0.97 = 0 Reorder the terms: -0.97 + 2x + -1x2 = 0 Solving -0.97 + 2x + -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'. 0.97 + -2x + x2 = 0 Move the constant term to the right: Add '-0.97' to each side of the equation. 0.97 + -2x + -0.97 + x2 = 0 + -0.97 Reorder the terms: 0.97 + -0.97 + -2x + x2 = 0 + -0.97 Combine like terms: 0.97 + -0.97 = 0.00 0.00 + -2x + x2 = 0 + -0.97 -2x + x2 = 0 + -0.97 Combine like terms: 0 + -0.97 = -0.97 -2x + x2 = -0.97 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 = -0.97 + 1 Reorder the terms: 1 + -2x + x2 = -0.97 + 1 Combine like terms: -0.97 + 1 = 0.03 1 + -2x + x2 = 0.03 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.03 Calculate the square root of the right side: 0.173205081 Break this problem into two subproblems by setting (x + -1) equal to 0.173205081 and -0.173205081.Subproblem 1
x + -1 = 0.173205081 Simplifying x + -1 = 0.173205081 Reorder the terms: -1 + x = 0.173205081 Solving -1 + x = 0.173205081 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 = 0.173205081 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.173205081 + 1 x = 0.173205081 + 1 Combine like terms: 0.173205081 + 1 = 1.173205081 x = 1.173205081 Simplifying x = 1.173205081Subproblem 2
x + -1 = -0.173205081 Simplifying x + -1 = -0.173205081 Reorder the terms: -1 + x = -0.173205081 Solving -1 + x = -0.173205081 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 = -0.173205081 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.173205081 + 1 x = -0.173205081 + 1 Combine like terms: -0.173205081 + 1 = 0.826794919 x = 0.826794919 Simplifying x = 0.826794919Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.173205081, 0.826794919}
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