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Simplifying 5x2 + -10x + -16 = 4x Reorder the terms: -16 + -10x + 5x2 = 4x Solving -16 + -10x + 5x2 = 4x Solving for variable 'x'. Reorder the terms: -16 + -10x + -4x + 5x2 = 4x + -4x Combine like terms: -10x + -4x = -14x -16 + -14x + 5x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -16 + -14x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.2 + -2.8x + x2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + -2.8x + 3.2 + x2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + -2.8x + x2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + -2.8x + x2 = 0 + 3.2 -2.8x + x2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 -2.8x + x2 = 3.2 The x term is -2.8x. Take half its coefficient (-1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. -2.8x + 1.96 + x2 = 3.2 + 1.96 Reorder the terms: 1.96 + -2.8x + x2 = 3.2 + 1.96 Combine like terms: 3.2 + 1.96 = 5.16 1.96 + -2.8x + x2 = 5.16 Factor a perfect square on the left side: (x + -1.4)(x + -1.4) = 5.16 Calculate the square root of the right side: 2.271563338 Break this problem into two subproblems by setting (x + -1.4) equal to 2.271563338 and -2.271563338.Subproblem 1
x + -1.4 = 2.271563338 Simplifying x + -1.4 = 2.271563338 Reorder the terms: -1.4 + x = 2.271563338 Solving -1.4 + x = 2.271563338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = 2.271563338 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = 2.271563338 + 1.4 x = 2.271563338 + 1.4 Combine like terms: 2.271563338 + 1.4 = 3.671563338 x = 3.671563338 Simplifying x = 3.671563338Subproblem 2
x + -1.4 = -2.271563338 Simplifying x + -1.4 = -2.271563338 Reorder the terms: -1.4 + x = -2.271563338 Solving -1.4 + x = -2.271563338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = -2.271563338 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = -2.271563338 + 1.4 x = -2.271563338 + 1.4 Combine like terms: -2.271563338 + 1.4 = -0.871563338 x = -0.871563338 Simplifying x = -0.871563338Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.671563338, -0.871563338}
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