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Simplifying -1x2 + 5.2x + -0.8 = 0 Reorder the terms: -0.8 + 5.2x + -1x2 = 0 Solving -0.8 + 5.2x + -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'. 0.8 + -5.2x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + -5.2x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + -5.2x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + -5.2x + x2 = 0 + -0.8 -5.2x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 -5.2x + x2 = -0.8 The x term is -5.2x. Take half its coefficient (-2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. -5.2x + 6.76 + x2 = -0.8 + 6.76 Reorder the terms: 6.76 + -5.2x + x2 = -0.8 + 6.76 Combine like terms: -0.8 + 6.76 = 5.96 6.76 + -5.2x + x2 = 5.96 Factor a perfect square on the left side: (x + -2.6)(x + -2.6) = 5.96 Calculate the square root of the right side: 2.441311123 Break this problem into two subproblems by setting (x + -2.6) equal to 2.441311123 and -2.441311123.Subproblem 1
x + -2.6 = 2.441311123 Simplifying x + -2.6 = 2.441311123 Reorder the terms: -2.6 + x = 2.441311123 Solving -2.6 + x = 2.441311123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + x = 2.441311123 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + x = 2.441311123 + 2.6 x = 2.441311123 + 2.6 Combine like terms: 2.441311123 + 2.6 = 5.041311123 x = 5.041311123 Simplifying x = 5.041311123Subproblem 2
x + -2.6 = -2.441311123 Simplifying x + -2.6 = -2.441311123 Reorder the terms: -2.6 + x = -2.441311123 Solving -2.6 + x = -2.441311123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + x = -2.441311123 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + x = -2.441311123 + 2.6 x = -2.441311123 + 2.6 Combine like terms: -2.441311123 + 2.6 = 0.158688877 x = 0.158688877 Simplifying x = 0.158688877Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.041311123, 0.158688877}
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