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Simplifying 7x2 + -14x + -87 = -9 Reorder the terms: -87 + -14x + 7x2 = -9 Solving -87 + -14x + 7x2 = -9 Solving for variable 'x'. Reorder the terms: -87 + 9 + -14x + 7x2 = -9 + 9 Combine like terms: -87 + 9 = -78 -78 + -14x + 7x2 = -9 + 9 Combine like terms: -9 + 9 = 0 -78 + -14x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -11.14285714 + -2x + x2 = 0 Move the constant term to the right: Add '11.14285714' to each side of the equation. -11.14285714 + -2x + 11.14285714 + x2 = 0 + 11.14285714 Reorder the terms: -11.14285714 + 11.14285714 + -2x + x2 = 0 + 11.14285714 Combine like terms: -11.14285714 + 11.14285714 = 0.00000000 0.00000000 + -2x + x2 = 0 + 11.14285714 -2x + x2 = 0 + 11.14285714 Combine like terms: 0 + 11.14285714 = 11.14285714 -2x + x2 = 11.14285714 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 = 11.14285714 + 1 Reorder the terms: 1 + -2x + x2 = 11.14285714 + 1 Combine like terms: 11.14285714 + 1 = 12.14285714 1 + -2x + x2 = 12.14285714 Factor a perfect square on the left side: (x + -1)(x + -1) = 12.14285714 Calculate the square root of the right side: 3.484660262 Break this problem into two subproblems by setting (x + -1) equal to 3.484660262 and -3.484660262.Subproblem 1
x + -1 = 3.484660262 Simplifying x + -1 = 3.484660262 Reorder the terms: -1 + x = 3.484660262 Solving -1 + x = 3.484660262 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 = 3.484660262 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.484660262 + 1 x = 3.484660262 + 1 Combine like terms: 3.484660262 + 1 = 4.484660262 x = 4.484660262 Simplifying x = 4.484660262Subproblem 2
x + -1 = -3.484660262 Simplifying x + -1 = -3.484660262 Reorder the terms: -1 + x = -3.484660262 Solving -1 + x = -3.484660262 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 = -3.484660262 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.484660262 + 1 x = -3.484660262 + 1 Combine like terms: -3.484660262 + 1 = -2.484660262 x = -2.484660262 Simplifying x = -2.484660262Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.484660262, -2.484660262}
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