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Simplifying 7x2 + -10x = 86 + 6x Reorder the terms: -10x + 7x2 = 86 + 6x Solving -10x + 7x2 = 86 + 6x Solving for variable 'x'. Reorder the terms: -86 + -10x + -6x + 7x2 = 86 + 6x + -86 + -6x Combine like terms: -10x + -6x = -16x -86 + -16x + 7x2 = 86 + 6x + -86 + -6x Reorder the terms: -86 + -16x + 7x2 = 86 + -86 + 6x + -6x Combine like terms: 86 + -86 = 0 -86 + -16x + 7x2 = 0 + 6x + -6x -86 + -16x + 7x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -86 + -16x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -12.28571429 + -2.285714286x + x2 = 0 Move the constant term to the right: Add '12.28571429' to each side of the equation. -12.28571429 + -2.285714286x + 12.28571429 + x2 = 0 + 12.28571429 Reorder the terms: -12.28571429 + 12.28571429 + -2.285714286x + x2 = 0 + 12.28571429 Combine like terms: -12.28571429 + 12.28571429 = 0.00000000 0.00000000 + -2.285714286x + x2 = 0 + 12.28571429 -2.285714286x + x2 = 0 + 12.28571429 Combine like terms: 0 + 12.28571429 = 12.28571429 -2.285714286x + x2 = 12.28571429 The x term is -2.285714286x. Take half its coefficient (-1.142857143). Square it (1.306122449) and add it to both sides. Add '1.306122449' to each side of the equation. -2.285714286x + 1.306122449 + x2 = 12.28571429 + 1.306122449 Reorder the terms: 1.306122449 + -2.285714286x + x2 = 12.28571429 + 1.306122449 Combine like terms: 12.28571429 + 1.306122449 = 13.591836739 1.306122449 + -2.285714286x + x2 = 13.591836739 Factor a perfect square on the left side: (x + -1.142857143)(x + -1.142857143) = 13.591836739 Calculate the square root of the right side: 3.686710829 Break this problem into two subproblems by setting (x + -1.142857143) equal to 3.686710829 and -3.686710829.Subproblem 1
x + -1.142857143 = 3.686710829 Simplifying x + -1.142857143 = 3.686710829 Reorder the terms: -1.142857143 + x = 3.686710829 Solving -1.142857143 + x = 3.686710829 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.142857143' to each side of the equation. -1.142857143 + 1.142857143 + x = 3.686710829 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + x = 3.686710829 + 1.142857143 x = 3.686710829 + 1.142857143 Combine like terms: 3.686710829 + 1.142857143 = 4.829567972 x = 4.829567972 Simplifying x = 4.829567972Subproblem 2
x + -1.142857143 = -3.686710829 Simplifying x + -1.142857143 = -3.686710829 Reorder the terms: -1.142857143 + x = -3.686710829 Solving -1.142857143 + x = -3.686710829 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.142857143' to each side of the equation. -1.142857143 + 1.142857143 + x = -3.686710829 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + x = -3.686710829 + 1.142857143 x = -3.686710829 + 1.142857143 Combine like terms: -3.686710829 + 1.142857143 = -2.543853686 x = -2.543853686 Simplifying x = -2.543853686Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.829567972, -2.543853686}
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