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Simplifying 10x2 + -11x + -56 = 5x2 Reorder the terms: -56 + -11x + 10x2 = 5x2 Solving -56 + -11x + 10x2 = 5x2 Solving for variable 'x'. Combine like terms: 10x2 + -5x2 = 5x2 -56 + -11x + 5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -56 + -11x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -11.2 + -2.2x + x2 = 0 Move the constant term to the right: Add '11.2' to each side of the equation. -11.2 + -2.2x + 11.2 + x2 = 0 + 11.2 Reorder the terms: -11.2 + 11.2 + -2.2x + x2 = 0 + 11.2 Combine like terms: -11.2 + 11.2 = 0.0 0.0 + -2.2x + x2 = 0 + 11.2 -2.2x + x2 = 0 + 11.2 Combine like terms: 0 + 11.2 = 11.2 -2.2x + x2 = 11.2 The x term is -2.2x. Take half its coefficient (-1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. -2.2x + 1.21 + x2 = 11.2 + 1.21 Reorder the terms: 1.21 + -2.2x + x2 = 11.2 + 1.21 Combine like terms: 11.2 + 1.21 = 12.41 1.21 + -2.2x + x2 = 12.41 Factor a perfect square on the left side: (x + -1.1)(x + -1.1) = 12.41 Calculate the square root of the right side: 3.522782991 Break this problem into two subproblems by setting (x + -1.1) equal to 3.522782991 and -3.522782991.Subproblem 1
x + -1.1 = 3.522782991 Simplifying x + -1.1 = 3.522782991 Reorder the terms: -1.1 + x = 3.522782991 Solving -1.1 + x = 3.522782991 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = 3.522782991 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = 3.522782991 + 1.1 x = 3.522782991 + 1.1 Combine like terms: 3.522782991 + 1.1 = 4.622782991 x = 4.622782991 Simplifying x = 4.622782991Subproblem 2
x + -1.1 = -3.522782991 Simplifying x + -1.1 = -3.522782991 Reorder the terms: -1.1 + x = -3.522782991 Solving -1.1 + x = -3.522782991 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = -3.522782991 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = -3.522782991 + 1.1 x = -3.522782991 + 1.1 Combine like terms: -3.522782991 + 1.1 = -2.422782991 x = -2.422782991 Simplifying x = -2.422782991Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.622782991, -2.422782991}
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