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Simplifying -1x2 + 19x + 26 = 0 Reorder the terms: 26 + 19x + -1x2 = 0 Solving 26 + 19x + -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'. -26 + -19x + x2 = 0 Move the constant term to the right: Add '26' to each side of the equation. -26 + -19x + 26 + x2 = 0 + 26 Reorder the terms: -26 + 26 + -19x + x2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + -19x + x2 = 0 + 26 -19x + x2 = 0 + 26 Combine like terms: 0 + 26 = 26 -19x + x2 = 26 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = 26 + 90.25 Reorder the terms: 90.25 + -19x + x2 = 26 + 90.25 Combine like terms: 26 + 90.25 = 116.25 90.25 + -19x + x2 = 116.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 116.25 Calculate the square root of the right side: 10.781929326 Break this problem into two subproblems by setting (x + -9.5) equal to 10.781929326 and -10.781929326.Subproblem 1
x + -9.5 = 10.781929326 Simplifying x + -9.5 = 10.781929326 Reorder the terms: -9.5 + x = 10.781929326 Solving -9.5 + x = 10.781929326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 10.781929326 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 10.781929326 + 9.5 x = 10.781929326 + 9.5 Combine like terms: 10.781929326 + 9.5 = 20.281929326 x = 20.281929326 Simplifying x = 20.281929326Subproblem 2
x + -9.5 = -10.781929326 Simplifying x + -9.5 = -10.781929326 Reorder the terms: -9.5 + x = -10.781929326 Solving -9.5 + x = -10.781929326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -10.781929326 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -10.781929326 + 9.5 x = -10.781929326 + 9.5 Combine like terms: -10.781929326 + 9.5 = -1.281929326 x = -1.281929326 Simplifying x = -1.281929326Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.281929326, -1.281929326}
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