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Simplifying x2 + 13x + -74 = 0 Reorder the terms: -74 + 13x + x2 = 0 Solving -74 + 13x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '74' to each side of the equation. -74 + 13x + 74 + x2 = 0 + 74 Reorder the terms: -74 + 74 + 13x + x2 = 0 + 74 Combine like terms: -74 + 74 = 0 0 + 13x + x2 = 0 + 74 13x + x2 = 0 + 74 Combine like terms: 0 + 74 = 74 13x + x2 = 74 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = 74 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 74 + 42.25 Combine like terms: 74 + 42.25 = 116.25 42.25 + 13x + x2 = 116.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 116.25 Calculate the square root of the right side: 10.781929326 Break this problem into two subproblems by setting (x + 6.5) equal to 10.781929326 and -10.781929326.Subproblem 1
x + 6.5 = 10.781929326 Simplifying x + 6.5 = 10.781929326 Reorder the terms: 6.5 + x = 10.781929326 Solving 6.5 + x = 10.781929326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 10.781929326 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 10.781929326 + -6.5 x = 10.781929326 + -6.5 Combine like terms: 10.781929326 + -6.5 = 4.281929326 x = 4.281929326 Simplifying x = 4.281929326Subproblem 2
x + 6.5 = -10.781929326 Simplifying x + 6.5 = -10.781929326 Reorder the terms: 6.5 + x = -10.781929326 Solving 6.5 + x = -10.781929326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -10.781929326 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -10.781929326 + -6.5 x = -10.781929326 + -6.5 Combine like terms: -10.781929326 + -6.5 = -17.281929326 x = -17.281929326 Simplifying x = -17.281929326Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.281929326, -17.281929326}
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