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Simplifying 19x2 + -30x + -8 = 0 Reorder the terms: -8 + -30x + 19x2 = 0 Solving -8 + -30x + 19x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. -0.4210526316 + -1.578947368x + x2 = 0 Move the constant term to the right: Add '0.4210526316' to each side of the equation. -0.4210526316 + -1.578947368x + 0.4210526316 + x2 = 0 + 0.4210526316 Reorder the terms: -0.4210526316 + 0.4210526316 + -1.578947368x + x2 = 0 + 0.4210526316 Combine like terms: -0.4210526316 + 0.4210526316 = 0.0000000000 0.0000000000 + -1.578947368x + x2 = 0 + 0.4210526316 -1.578947368x + x2 = 0 + 0.4210526316 Combine like terms: 0 + 0.4210526316 = 0.4210526316 -1.578947368x + x2 = 0.4210526316 The x term is -1.578947368x. Take half its coefficient (-0.789473684). Square it (0.6232686977) and add it to both sides. Add '0.6232686977' to each side of the equation. -1.578947368x + 0.6232686977 + x2 = 0.4210526316 + 0.6232686977 Reorder the terms: 0.6232686977 + -1.578947368x + x2 = 0.4210526316 + 0.6232686977 Combine like terms: 0.4210526316 + 0.6232686977 = 1.0443213293 0.6232686977 + -1.578947368x + x2 = 1.0443213293 Factor a perfect square on the left side: (x + -0.789473684)(x + -0.789473684) = 1.0443213293 Calculate the square root of the right side: 1.021920412 Break this problem into two subproblems by setting (x + -0.789473684) equal to 1.021920412 and -1.021920412.Subproblem 1
x + -0.789473684 = 1.021920412 Simplifying x + -0.789473684 = 1.021920412 Reorder the terms: -0.789473684 + x = 1.021920412 Solving -0.789473684 + x = 1.021920412 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.789473684' to each side of the equation. -0.789473684 + 0.789473684 + x = 1.021920412 + 0.789473684 Combine like terms: -0.789473684 + 0.789473684 = 0.000000000 0.000000000 + x = 1.021920412 + 0.789473684 x = 1.021920412 + 0.789473684 Combine like terms: 1.021920412 + 0.789473684 = 1.811394096 x = 1.811394096 Simplifying x = 1.811394096Subproblem 2
x + -0.789473684 = -1.021920412 Simplifying x + -0.789473684 = -1.021920412 Reorder the terms: -0.789473684 + x = -1.021920412 Solving -0.789473684 + x = -1.021920412 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.789473684' to each side of the equation. -0.789473684 + 0.789473684 + x = -1.021920412 + 0.789473684 Combine like terms: -0.789473684 + 0.789473684 = 0.000000000 0.000000000 + x = -1.021920412 + 0.789473684 x = -1.021920412 + 0.789473684 Combine like terms: -1.021920412 + 0.789473684 = -0.232446728 x = -0.232446728 Simplifying x = -0.232446728Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.811394096, -0.232446728}
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