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Simplifying 7x2 + 14x + -10 = 6 Reorder the terms: -10 + 14x + 7x2 = 6 Solving -10 + 14x + 7x2 = 6 Solving for variable 'x'. Reorder the terms: -10 + -6 + 14x + 7x2 = 6 + -6 Combine like terms: -10 + -6 = -16 -16 + 14x + 7x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -16 + 14x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.285714286 + 2x + x2 = 0 Move the constant term to the right: Add '2.285714286' to each side of the equation. -2.285714286 + 2x + 2.285714286 + x2 = 0 + 2.285714286 Reorder the terms: -2.285714286 + 2.285714286 + 2x + x2 = 0 + 2.285714286 Combine like terms: -2.285714286 + 2.285714286 = 0.000000000 0.000000000 + 2x + x2 = 0 + 2.285714286 2x + x2 = 0 + 2.285714286 Combine like terms: 0 + 2.285714286 = 2.285714286 2x + x2 = 2.285714286 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 2.285714286 + 1 Reorder the terms: 1 + 2x + x2 = 2.285714286 + 1 Combine like terms: 2.285714286 + 1 = 3.285714286 1 + 2x + x2 = 3.285714286 Factor a perfect square on the left side: (x + 1)(x + 1) = 3.285714286 Calculate the square root of the right side: 1.812653934 Break this problem into two subproblems by setting (x + 1) equal to 1.812653934 and -1.812653934.Subproblem 1
x + 1 = 1.812653934 Simplifying x + 1 = 1.812653934 Reorder the terms: 1 + x = 1.812653934 Solving 1 + x = 1.812653934 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.812653934 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.812653934 + -1 x = 1.812653934 + -1 Combine like terms: 1.812653934 + -1 = 0.812653934 x = 0.812653934 Simplifying x = 0.812653934Subproblem 2
x + 1 = -1.812653934 Simplifying x + 1 = -1.812653934 Reorder the terms: 1 + x = -1.812653934 Solving 1 + x = -1.812653934 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.812653934 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.812653934 + -1 x = -1.812653934 + -1 Combine like terms: -1.812653934 + -1 = -2.812653934 x = -2.812653934 Simplifying x = -2.812653934Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.812653934, -2.812653934}
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