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Simplifying 0.25x2 + 1.3x + -2 = 0 Reorder the terms: -2 + 1.3x + 0.25x2 = 0 Solving -2 + 1.3x + 0.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. -8 + 5.2x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 5.2x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 5.2x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 5.2x + x2 = 0 + 8 5.2x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 5.2x + x2 = 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 = 8 + 6.76 Reorder the terms: 6.76 + 5.2x + x2 = 8 + 6.76 Combine like terms: 8 + 6.76 = 14.76 6.76 + 5.2x + x2 = 14.76 Factor a perfect square on the left side: (x + 2.6)(x + 2.6) = 14.76 Calculate the square root of the right side: 3.841874542 Break this problem into two subproblems by setting (x + 2.6) equal to 3.841874542 and -3.841874542.Subproblem 1
x + 2.6 = 3.841874542 Simplifying x + 2.6 = 3.841874542 Reorder the terms: 2.6 + x = 3.841874542 Solving 2.6 + x = 3.841874542 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 = 3.841874542 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + x = 3.841874542 + -2.6 x = 3.841874542 + -2.6 Combine like terms: 3.841874542 + -2.6 = 1.241874542 x = 1.241874542 Simplifying x = 1.241874542Subproblem 2
x + 2.6 = -3.841874542 Simplifying x + 2.6 = -3.841874542 Reorder the terms: 2.6 + x = -3.841874542 Solving 2.6 + x = -3.841874542 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 = -3.841874542 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + x = -3.841874542 + -2.6 x = -3.841874542 + -2.6 Combine like terms: -3.841874542 + -2.6 = -6.441874542 x = -6.441874542 Simplifying x = -6.441874542Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.241874542, -6.441874542}
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