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Simplifying 7x2 + 30x + -8 = 0 Reorder the terms: -8 + 30x + 7x2 = 0 Solving -8 + 30x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.142857143 + 4.285714286x + x2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + 4.285714286x + 1.142857143 + x2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + 4.285714286x + x2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + 4.285714286x + x2 = 0 + 1.142857143 4.285714286x + x2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 4.285714286x + x2 = 1.142857143 The x term is 4.285714286x. Take half its coefficient (2.142857143). Square it (4.591836735) and add it to both sides. Add '4.591836735' to each side of the equation. 4.285714286x + 4.591836735 + x2 = 1.142857143 + 4.591836735 Reorder the terms: 4.591836735 + 4.285714286x + x2 = 1.142857143 + 4.591836735 Combine like terms: 1.142857143 + 4.591836735 = 5.734693878 4.591836735 + 4.285714286x + x2 = 5.734693878 Factor a perfect square on the left side: (x + 2.142857143)(x + 2.142857143) = 5.734693878 Calculate the square root of the right side: 2.394722088 Break this problem into two subproblems by setting (x + 2.142857143) equal to 2.394722088 and -2.394722088.Subproblem 1
x + 2.142857143 = 2.394722088 Simplifying x + 2.142857143 = 2.394722088 Reorder the terms: 2.142857143 + x = 2.394722088 Solving 2.142857143 + x = 2.394722088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.142857143' to each side of the equation. 2.142857143 + -2.142857143 + x = 2.394722088 + -2.142857143 Combine like terms: 2.142857143 + -2.142857143 = 0.000000000 0.000000000 + x = 2.394722088 + -2.142857143 x = 2.394722088 + -2.142857143 Combine like terms: 2.394722088 + -2.142857143 = 0.251864945 x = 0.251864945 Simplifying x = 0.251864945Subproblem 2
x + 2.142857143 = -2.394722088 Simplifying x + 2.142857143 = -2.394722088 Reorder the terms: 2.142857143 + x = -2.394722088 Solving 2.142857143 + x = -2.394722088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.142857143' to each side of the equation. 2.142857143 + -2.142857143 + x = -2.394722088 + -2.142857143 Combine like terms: 2.142857143 + -2.142857143 = 0.000000000 0.000000000 + x = -2.394722088 + -2.142857143 x = -2.394722088 + -2.142857143 Combine like terms: -2.394722088 + -2.142857143 = -4.537579231 x = -4.537579231 Simplifying x = -4.537579231Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.251864945, -4.537579231}
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