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Simplifying x2 = 10 + x(7 + -9x) x2 = 10 + (7 * x + -9x * x) x2 = 10 + (7x + -9x2) Solving x2 = 10 + 7x + -9x2 Solving for variable 'x'. Reorder the terms: -10 + -7x + x2 + 9x2 = 10 + 7x + -9x2 + -10 + -7x + 9x2 Combine like terms: x2 + 9x2 = 10x2 -10 + -7x + 10x2 = 10 + 7x + -9x2 + -10 + -7x + 9x2 Reorder the terms: -10 + -7x + 10x2 = 10 + -10 + 7x + -7x + -9x2 + 9x2 Combine like terms: 10 + -10 = 0 -10 + -7x + 10x2 = 0 + 7x + -7x + -9x2 + 9x2 -10 + -7x + 10x2 = 7x + -7x + -9x2 + 9x2 Combine like terms: 7x + -7x = 0 -10 + -7x + 10x2 = 0 + -9x2 + 9x2 -10 + -7x + 10x2 = -9x2 + 9x2 Combine like terms: -9x2 + 9x2 = 0 -10 + -7x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1 + -0.7x + x2 = 0.0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.7x + 1 + x2 = 0.0 + 1 Reorder the terms: -1 + 1 + -0.7x + x2 = 0.0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.7x + x2 = 0.0 + 1 -0.7x + x2 = 0.0 + 1 Combine like terms: 0.0 + 1 = 1 -0.7x + x2 = 1 The x term is -0.7x. Take half its coefficient (-0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. -0.7x + 0.1225 + x2 = 1 + 0.1225 Reorder the terms: 0.1225 + -0.7x + x2 = 1 + 0.1225 Combine like terms: 1 + 0.1225 = 1.1225 0.1225 + -0.7x + x2 = 1.1225 Factor a perfect square on the left side: (x + -0.35)(x + -0.35) = 1.1225 Calculate the square root of the right side: 1.059481005 Break this problem into two subproblems by setting (x + -0.35) equal to 1.059481005 and -1.059481005.Subproblem 1
x + -0.35 = 1.059481005 Simplifying x + -0.35 = 1.059481005 Reorder the terms: -0.35 + x = 1.059481005 Solving -0.35 + x = 1.059481005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + x = 1.059481005 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + x = 1.059481005 + 0.35 x = 1.059481005 + 0.35 Combine like terms: 1.059481005 + 0.35 = 1.409481005 x = 1.409481005 Simplifying x = 1.409481005Subproblem 2
x + -0.35 = -1.059481005 Simplifying x + -0.35 = -1.059481005 Reorder the terms: -0.35 + x = -1.059481005 Solving -0.35 + x = -1.059481005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + x = -1.059481005 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + x = -1.059481005 + 0.35 x = -1.059481005 + 0.35 Combine like terms: -1.059481005 + 0.35 = -0.709481005 x = -0.709481005 Simplifying x = -0.709481005Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.409481005, -0.709481005}
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